Rajesh Narayanan - Academia.edu (original) (raw)

Papers by Rajesh Narayanan

Research paper thumbnail of Effects of local moments on a Mott transition

In this work, we study the influence of interacting (long-ranged) local moments on a Mott-transit... more In this work, we study the influence of interacting (long-ranged) local moments on a Mott-transition. We show that at low temperatures even in the presence of these local moments the Mott-transition remains first order. However, at higher temperatures the Mott tricritical point is depressed. We also show that the transitions lines are bent due to the effects of these local moment fluctuations. Finally, we study the behavior of various thermodynamic observables as we scan the various parts of the phase diagram. These results were obtained by using a Hubbard- Heisenberg model with a local Coulomb repulsion and infinite ranged spin interactions. The model is solved by allying dynamical mean field theory equations with the slave- rotor technique.

Research paper thumbnail of Influence of superohmic dissipation on a disordered quantum critical point

We investigate the combined influence of quenched randomness and dissipation on a quantum critica... more We investigate the combined influence of quenched randomness and dissipation on a quantum critical point with O(N) order-parameter symmetry. Utilizing a strong-disorder renormalization group, we determine the critical behavior in one space dimension exactly. For superohmic dissipation, we find a Kosterlitz-Thouless type transition with conventional (power-law) dynamical scaling. The dynamical critical exponent depends on the spectral density of the dissipative baths. We also discuss the Griffiths singularities, and we determine observables.

Research paper thumbnail of Anomalously Elastic Intermediate Phase in Randomly Layered Superfluids, Superconductors, and Planar Magnets

Physical Review Letters, 2010

We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase... more We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase between the conventional ferromagnetic low-temperature and paramagnetic high-temperature phases. In this intermediate phase, which is part of the Griffiths region, the spin-wave stiffness perpendicular to the random layers displays anomalous scaling behavior, with a continuously variable anomalous exponent, while the magnetization and the stiffness parallel to the layers both remain finite. Analogous results hold for superfluids and superconductors. We study the two phase transitions into the anomalous elastic phase, and we discuss the universality of these results, and implications of finite sample size as well as possible experiments.

Research paper thumbnail of Order-parameter symmetry and mode-coupling effects at dirty superconducting quantum phase transitions

Physical Review B, 2004

We derive an order-parameter field theory for a quantum phase transition between a disordered met... more We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-s-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an effective long-range interaction between the anomalous density fluctuations which is reflected in singularities in the free energy functional. However, this long-range interaction is not strong enough to suppress disorder fluctuations. The asymptotic critical region is characterized by run-away flow to large disorder. For weak coupling, this asymptotic region is very narrow. It is preempted by a wide crossover regime with mean-field critical behavior and, in the p-wave case, logarithmic corrections to scaling in all dimensions.

Research paper thumbnail of Order parameter symmetry and mode coupling effects at dirty superconducting quantum phase transitions

We derive an order-parameter field theory for a quantum phase transition between a disordered met... more We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-s-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an effective long-range interaction between the anomalous density fluctuations which is reflected in singularities in the free energy functional. However, this long-range interaction is not strong enough to suppress disorder fluctuations. The asymptotic critical region is characterized by run-away flow to large disorder. For weak coupling, this region is very narrow, and it is preempted by a wide crossover regime with mean-field critical behavior and, in the p-wave case, logarithmic corrections to scaling in all dimensions. The results are discussed from a general mode-coupling point of view and in relation to recent experiments.

Research paper thumbnail of Effect of rare locally ordered regions on a disordered itinerant quantum antiferromagnet with cubic anisotropy

Physical Review B, 2001

We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in th... more We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We derive an effective action where these rare regions are described in terms of static annealed disorder. A one loop renormalization group analysis of the effective action shows that for order parameter dimensions p < 4 the rare regions destroy the conventional critical behavior. For order parameter dimensions p > 4 the critical behavior is not influenced by the rare regions, it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition in this system.

Research paper thumbnail of Infinite randomness and quantum Griffiths effects in a classical system: The randomly layered Heisenberg magnet

Physical Review B, 2010

We investigate the phase transition in a three-dimensional classical Heisenberg magnet with plana... more We investigate the phase transition in a three-dimensional classical Heisenberg magnet with planar defects, i.e., disorder perfectly correlated in two dimensions. By applying a strong-disorder renormalization group, we show that the critical point has exotic infinite-randomness character. It is accompanied by strong power-law Griffiths singularities. We compute various thermodynamic observables paying particular attention to finite-size effects relevant for an experimental verification of our theory. We also study the critical dynamics within a Langevin equation approach and find it extremely slow. At the critical point, the autocorrelation function decays only logarithmically with time while it follows a nonuniversal power-law in the Griffiths phase.

Research paper thumbnail of Critical behavior of disordered quantum magnets: The relevance of rare regions

Physical Review B, 1999

The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets... more The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets and ferromagnets are considered. Particular attention is paid to locally ordered spatial regions that are formed in the presence of quenched disorder even when the bulk system is still in the paramagnetic phase. These rare regions or local moments are reflected in the existence of spatially inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive an effective theory that takes into account small fluctuations around all of these saddle points. The resulting free energy functional contains a new term in addition to those obtained within the conventional perturbative approach, and it comprises what would be considered non-perturbative effects within the latter. A renormalization group analysis shows that in the case of antiferromagnets, the previously found critical fixed point is unstable with respect to this new term, and that no stable critical fixed point exists at one-loop order. This is contrasted with the case of itinerant ferromagnets, where we find that the previously found critical behavior is unaffected by the rare regions due to an effective long-ranged interaction between the order parameter fluctuations.

Research paper thumbnail of Influence of Rare Regions on Magnetic Quantum Phase Transitions

Physical Review Letters, 1999

The effects of quenched disorder on the critical properties of itinerant quantum magnets are cons... more The effects of quenched disorder on the critical properties of itinerant quantum magnets are considered. Particular attention is paid to locally ordered rare regions that are formed in the presence of quenched disorder even when the bulk system is still in the nonmagnetic phase. It is shown that these local moments or instantons destroy the previously found critical fixed point in the case of antiferromagnets. In the case of itinerant ferromagnets, the critical behavior is unaffected by the rare regions due to an effective long-range interaction between the order parameter fluctuations.

Research paper thumbnail of Evidence for power-law Griffiths singularities in a layered Heisenberg magnet

Journal of Physics: Conference Series, 2011

We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent stro... more We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent strong-disorder renormalization group approach [Phys. Rev. B 81, 144407 (2010)] predicted that the critical point in this system is of exotic infinite-randomness type and is accompanied by strong power-law Griffiths singularities. Here, we report results of Monte-Carlo simulations that provide numerical evidence in support of these predictions. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. In addition, we calculate the time autocorrelation function of the spins. It features a very slow decay in the Griffiths phase, following a non-universal power law in time.

Research paper thumbnail of Influence of super-ohmic dissipation on a disordered quantum critical point

Journal of Physics-condensed Matter, 2011

We investigate the combined influence of quenched randomness and dissipation on a quantum critica... more We investigate the combined influence of quenched randomness and dissipation on a quantum critical point with O(N) order-parameter symmetry. Utilizing a strong-disorder renormalization group, we determine the critical behavior in one space dimension exactly. For super-ohmic dissipation, we find a Kosterlitz-Thouless type transition with conventional (power-law) dynamical scaling. The dynamical critical exponent depends on the spectral density of the dissipative baths. We also discuss the Griffiths singularities, and we determine observables.

Research paper thumbnail of Evidence for power-law Griffiths singularities in a layered Heisenberg magnet

We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent stro... more We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent strong-disorder renormalization group approach [Phys. Rev. B 81, 144407 (2010)] predicted that the critical point in this system is of exotic infinite-randomness type and is accompanied by strong power-law Griffiths singularities. Here, we report results of Monte-Carlo simulations that provide numerical evidence in support of these predictions. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. In addition, we calculate the time autocorrelation function of the spins. It features a very slow decay in the Griffiths phase, following a non-universal power law in time.

Research paper thumbnail of An Anomalously Elastic, Intermediate Phase in Randomly Layered Planar Magnets, Superfluids, and Superconductors

We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase... more We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase between the conventional ferromagnetic low-temperature and paramagnetic high-temperature phases. In this intermediate phase, which is part of the Griffiths region, the spin-wave stiffness perpendicular to the random layers displays anomalous scaling behavior, with a continuously variable anomalous exponent, while the magnetization and the stiffness parallel to the layers both remain finite. Analogous results hold for superfluids and superconductors. We study the two phase transitions into the anomalous elastic phase, and we discuss the universality of these results, and implications of finite sample size as well as possible experiments.

Research paper thumbnail of The effect of rare regions on a disordered itinerant quantum antiferromagnet with cubic anisotropy

Physical Review B, 2000

We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in th... more We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We derive an effective action where these rare regions are described in terms of static annealed disorder. A one loop renormalization group analysis of the effective action shows that for order parameter dimensions p<4p<4p<4 the rare regions destroy the conventional critical behavior. For order parameter dimensions p>4p>4p>4 the critical behavior is not influenced by the rare regions, it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition in this system.

Research paper thumbnail of Localised zero-energy modes in the Kitaev model with vacancy-disorder

We study the effects of vacancy disorder on the Kitaev model defined on a hexagonal lattice. We s... more We study the effects of vacancy disorder on the Kitaev model defined on a hexagonal lattice. We show that the vacancy disorder induces a zero-mode that is localized at the defect site. We derive analytical forms for these localized wave functions in both the gapped and gapless phases of the Kitaev model. We conjecture that the vacancy disorder can be utilized as a probe of the quantum phase transition (from the gapped to gapless phases) in this model. The behavior of the Inverse Participation Ratio (IPR) in the gapless phase and across the transition is also studied numerically. Comments are made about the behavior of site-site entanglement in the single particle states for the case of a single vacancy.

Research paper thumbnail of Lessons gained from test beds of ad hoc networks and perspectives

Yvon Gourhant, François Jan France Telecom, Division R&amp;amp;amp;amp;amp;amp;amp;D 2 avenue... more Yvon Gourhant, François Jan France Telecom, Division R&amp;amp;amp;amp;amp;amp;amp;D 2 avenue Pierre Marzin 22307 Lannion Cedex, FRANCE Tel: +33 2 96 05 39 53 yvon.gourhant@francetelecom.com ... Tinku Mohamed Rasheed, Riadh Kortebi France Telecom, Division R&amp;amp;amp;amp;amp;amp;amp;D 2 avenue Pierre ...

Research paper thumbnail of Effects of local moments on a Mott transition

In this work, we study the influence of interacting (long-ranged) local moments on a Mott-transit... more In this work, we study the influence of interacting (long-ranged) local moments on a Mott-transition. We show that at low temperatures even in the presence of these local moments the Mott-transition remains first order. However, at higher temperatures the Mott tricritical point is depressed. We also show that the transitions lines are bent due to the effects of these local moment fluctuations. Finally, we study the behavior of various thermodynamic observables as we scan the various parts of the phase diagram. These results were obtained by using a Hubbard- Heisenberg model with a local Coulomb repulsion and infinite ranged spin interactions. The model is solved by allying dynamical mean field theory equations with the slave- rotor technique.

Research paper thumbnail of Influence of superohmic dissipation on a disordered quantum critical point

We investigate the combined influence of quenched randomness and dissipation on a quantum critica... more We investigate the combined influence of quenched randomness and dissipation on a quantum critical point with O(N) order-parameter symmetry. Utilizing a strong-disorder renormalization group, we determine the critical behavior in one space dimension exactly. For superohmic dissipation, we find a Kosterlitz-Thouless type transition with conventional (power-law) dynamical scaling. The dynamical critical exponent depends on the spectral density of the dissipative baths. We also discuss the Griffiths singularities, and we determine observables.

Research paper thumbnail of Anomalously Elastic Intermediate Phase in Randomly Layered Superfluids, Superconductors, and Planar Magnets

Physical Review Letters, 2010

We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase... more We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase between the conventional ferromagnetic low-temperature and paramagnetic high-temperature phases. In this intermediate phase, which is part of the Griffiths region, the spin-wave stiffness perpendicular to the random layers displays anomalous scaling behavior, with a continuously variable anomalous exponent, while the magnetization and the stiffness parallel to the layers both remain finite. Analogous results hold for superfluids and superconductors. We study the two phase transitions into the anomalous elastic phase, and we discuss the universality of these results, and implications of finite sample size as well as possible experiments.

Research paper thumbnail of Order-parameter symmetry and mode-coupling effects at dirty superconducting quantum phase transitions

Physical Review B, 2004

We derive an order-parameter field theory for a quantum phase transition between a disordered met... more We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-s-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an effective long-range interaction between the anomalous density fluctuations which is reflected in singularities in the free energy functional. However, this long-range interaction is not strong enough to suppress disorder fluctuations. The asymptotic critical region is characterized by run-away flow to large disorder. For weak coupling, this asymptotic region is very narrow. It is preempted by a wide crossover regime with mean-field critical behavior and, in the p-wave case, logarithmic corrections to scaling in all dimensions.

Research paper thumbnail of Order parameter symmetry and mode coupling effects at dirty superconducting quantum phase transitions

We derive an order-parameter field theory for a quantum phase transition between a disordered met... more We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-s-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an effective long-range interaction between the anomalous density fluctuations which is reflected in singularities in the free energy functional. However, this long-range interaction is not strong enough to suppress disorder fluctuations. The asymptotic critical region is characterized by run-away flow to large disorder. For weak coupling, this region is very narrow, and it is preempted by a wide crossover regime with mean-field critical behavior and, in the p-wave case, logarithmic corrections to scaling in all dimensions. The results are discussed from a general mode-coupling point of view and in relation to recent experiments.

Research paper thumbnail of Effect of rare locally ordered regions on a disordered itinerant quantum antiferromagnet with cubic anisotropy

Physical Review B, 2001

We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in th... more We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We derive an effective action where these rare regions are described in terms of static annealed disorder. A one loop renormalization group analysis of the effective action shows that for order parameter dimensions p < 4 the rare regions destroy the conventional critical behavior. For order parameter dimensions p > 4 the critical behavior is not influenced by the rare regions, it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition in this system.

Research paper thumbnail of Infinite randomness and quantum Griffiths effects in a classical system: The randomly layered Heisenberg magnet

Physical Review B, 2010

We investigate the phase transition in a three-dimensional classical Heisenberg magnet with plana... more We investigate the phase transition in a three-dimensional classical Heisenberg magnet with planar defects, i.e., disorder perfectly correlated in two dimensions. By applying a strong-disorder renormalization group, we show that the critical point has exotic infinite-randomness character. It is accompanied by strong power-law Griffiths singularities. We compute various thermodynamic observables paying particular attention to finite-size effects relevant for an experimental verification of our theory. We also study the critical dynamics within a Langevin equation approach and find it extremely slow. At the critical point, the autocorrelation function decays only logarithmically with time while it follows a nonuniversal power-law in the Griffiths phase.

Research paper thumbnail of Critical behavior of disordered quantum magnets: The relevance of rare regions

Physical Review B, 1999

The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets... more The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets and ferromagnets are considered. Particular attention is paid to locally ordered spatial regions that are formed in the presence of quenched disorder even when the bulk system is still in the paramagnetic phase. These rare regions or local moments are reflected in the existence of spatially inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive an effective theory that takes into account small fluctuations around all of these saddle points. The resulting free energy functional contains a new term in addition to those obtained within the conventional perturbative approach, and it comprises what would be considered non-perturbative effects within the latter. A renormalization group analysis shows that in the case of antiferromagnets, the previously found critical fixed point is unstable with respect to this new term, and that no stable critical fixed point exists at one-loop order. This is contrasted with the case of itinerant ferromagnets, where we find that the previously found critical behavior is unaffected by the rare regions due to an effective long-ranged interaction between the order parameter fluctuations.

Research paper thumbnail of Influence of Rare Regions on Magnetic Quantum Phase Transitions

Physical Review Letters, 1999

The effects of quenched disorder on the critical properties of itinerant quantum magnets are cons... more The effects of quenched disorder on the critical properties of itinerant quantum magnets are considered. Particular attention is paid to locally ordered rare regions that are formed in the presence of quenched disorder even when the bulk system is still in the nonmagnetic phase. It is shown that these local moments or instantons destroy the previously found critical fixed point in the case of antiferromagnets. In the case of itinerant ferromagnets, the critical behavior is unaffected by the rare regions due to an effective long-range interaction between the order parameter fluctuations.

Research paper thumbnail of Evidence for power-law Griffiths singularities in a layered Heisenberg magnet

Journal of Physics: Conference Series, 2011

We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent stro... more We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent strong-disorder renormalization group approach [Phys. Rev. B 81, 144407 (2010)] predicted that the critical point in this system is of exotic infinite-randomness type and is accompanied by strong power-law Griffiths singularities. Here, we report results of Monte-Carlo simulations that provide numerical evidence in support of these predictions. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. In addition, we calculate the time autocorrelation function of the spins. It features a very slow decay in the Griffiths phase, following a non-universal power law in time.

Research paper thumbnail of Influence of super-ohmic dissipation on a disordered quantum critical point

Journal of Physics-condensed Matter, 2011

We investigate the combined influence of quenched randomness and dissipation on a quantum critica... more We investigate the combined influence of quenched randomness and dissipation on a quantum critical point with O(N) order-parameter symmetry. Utilizing a strong-disorder renormalization group, we determine the critical behavior in one space dimension exactly. For super-ohmic dissipation, we find a Kosterlitz-Thouless type transition with conventional (power-law) dynamical scaling. The dynamical critical exponent depends on the spectral density of the dissipative baths. We also discuss the Griffiths singularities, and we determine observables.

Research paper thumbnail of Evidence for power-law Griffiths singularities in a layered Heisenberg magnet

We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent stro... more We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent strong-disorder renormalization group approach [Phys. Rev. B 81, 144407 (2010)] predicted that the critical point in this system is of exotic infinite-randomness type and is accompanied by strong power-law Griffiths singularities. Here, we report results of Monte-Carlo simulations that provide numerical evidence in support of these predictions. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. In addition, we calculate the time autocorrelation function of the spins. It features a very slow decay in the Griffiths phase, following a non-universal power law in time.

Research paper thumbnail of An Anomalously Elastic, Intermediate Phase in Randomly Layered Planar Magnets, Superfluids, and Superconductors

We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase... more We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase between the conventional ferromagnetic low-temperature and paramagnetic high-temperature phases. In this intermediate phase, which is part of the Griffiths region, the spin-wave stiffness perpendicular to the random layers displays anomalous scaling behavior, with a continuously variable anomalous exponent, while the magnetization and the stiffness parallel to the layers both remain finite. Analogous results hold for superfluids and superconductors. We study the two phase transitions into the anomalous elastic phase, and we discuss the universality of these results, and implications of finite sample size as well as possible experiments.

Research paper thumbnail of The effect of rare regions on a disordered itinerant quantum antiferromagnet with cubic anisotropy

Physical Review B, 2000

We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in th... more We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We derive an effective action where these rare regions are described in terms of static annealed disorder. A one loop renormalization group analysis of the effective action shows that for order parameter dimensions p<4p<4p<4 the rare regions destroy the conventional critical behavior. For order parameter dimensions p>4p>4p>4 the critical behavior is not influenced by the rare regions, it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition in this system.

Research paper thumbnail of Localised zero-energy modes in the Kitaev model with vacancy-disorder

We study the effects of vacancy disorder on the Kitaev model defined on a hexagonal lattice. We s... more We study the effects of vacancy disorder on the Kitaev model defined on a hexagonal lattice. We show that the vacancy disorder induces a zero-mode that is localized at the defect site. We derive analytical forms for these localized wave functions in both the gapped and gapless phases of the Kitaev model. We conjecture that the vacancy disorder can be utilized as a probe of the quantum phase transition (from the gapped to gapless phases) in this model. The behavior of the Inverse Participation Ratio (IPR) in the gapless phase and across the transition is also studied numerically. Comments are made about the behavior of site-site entanglement in the single particle states for the case of a single vacancy.

Research paper thumbnail of Lessons gained from test beds of ad hoc networks and perspectives

Yvon Gourhant, François Jan France Telecom, Division R&amp;amp;amp;amp;amp;amp;amp;D 2 avenue... more Yvon Gourhant, François Jan France Telecom, Division R&amp;amp;amp;amp;amp;amp;amp;D 2 avenue Pierre Marzin 22307 Lannion Cedex, FRANCE Tel: +33 2 96 05 39 53 yvon.gourhant@francetelecom.com ... Tinku Mohamed Rasheed, Riadh Kortebi France Telecom, Division R&amp;amp;amp;amp;amp;amp;amp;D 2 avenue Pierre ...