Shika Rachel - Academia.edu (original) (raw)
Papers by Shika Rachel
Physical Review B, 2009
We identify and investigate the new parameter regime of small charge solitons in one-dimensional ... more We identify and investigate the new parameter regime of small charge solitons in one-dimensional arrays of Josephson junctions. We obtain the dispersion relation of the soliton and show that it unexpectedly flattens in the outer region of the Brillouin zone. We demonstrate Lorentz contraction of the soliton in the middle of the Brillouin zone as well as broadening of the soliton in the flat band regime.
Physical Review B, 2007
To begin with, we introduce several exact models for SU͑3͒ spin chains: First is a translationall... more To begin with, we introduce several exact models for SU͑3͒ spin chains: First is a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a threefold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3 of SU͑3͒ if the original spins of the model transform under representation 3. Second is a family of parent Hamiltonians for valence bond solids of SU͑3͒ chains with spin representations 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement and, hence, a Haldane gap in the excitation spectrum. We generalize some of our models to SU͑n͒. Finally, we use the emerging rules for the construction of valence bond solid states to argue that models of antiferromagnetic chains of SU͑n͒ spins, in general, possess a Haldane gap if the spins transform under a representation corresponding to a Young tableau consisting of a number of boxes which is divisible by n. If and n have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If and n have a common divisor different from n, it will depend on the specifics of the model including the range of the interaction.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2013
Motivated by the recent progress in engineering artificial non-Abelian gauge fields for ultracold... more Motivated by the recent progress in engineering artificial non-Abelian gauge fields for ultracold fermions in optical lattices, we investigate the time-reversal-invariant Hofstadter-Hubbard model. We include an additional staggered lattice potential and an artificial Rashba-type spin-orbit coupling term available in experiment. Without interactions, the system can be either a (semi)-metal, a normal or a topological insulator, and we present the non-Abelian generalization of the Hofstadter butterfly. Using a combination of real-space dynamical mean-field theory (RDMFT), analytical arguments, and Monte-Carlo simulations we study the effect of strong on-site interactions. We determine the interacting phase diagram, and discuss a scenario of an interactioninduced transition from normal to topological insulator. At half-filling and large interactions, the system is described by a quantum spin Hamiltonian, which exhibits exotic magnetic order due to the interplay of Rashba-type spinorbit coupling and the artificial time-reversal-invariant magnetic field term. We determine the magnetic phase diagram: both for the itinerant model using RDMFT and for the corresponding spin model in the classical limit using Monte-Carlo simulations.
Physical Review B, 2010
We systematically study the phase diagram of S = 2 spin chain by means of density-matrix renormal... more We systematically study the phase diagram of S = 2 spin chain by means of density-matrix renormalization group and exact diagonalization. We confirm the presence of a dimer phase in the AKLT-SZH model and find that the whole phase boundary between dimer and SZH phases, including the multicritical point, is a critical line with central charge c = 5/2. Finally, we propose and confirm that this line corresponds to SO(5)1 Wess-Zumino-Witten conformal field theory.
We show that the concept of bipartite fluctuations F provides a very efficient tool to detect qua... more We show that the concept of bipartite fluctuations F provides a very efficient tool to detect quantum phase transitions in strongly correlated systems. Using state of the art numerical techniques complemented with analytical arguments, we investigate paradigmatic examples for both quantum spins and bosons. As compared to the von Neumann entanglement entropy, we observe that F allows to find quantum critical points with a much better accuracy in one dimension. We further demonstrate that F can be successfully applied to the detection of quantum criticality in higher dimensions with no prior knowledge of the universality class of the transition. Promising approaches to experimentally access fluctuations are discussed for quantum antiferromagnets and cold gases.
We introduce several exact models for SU͑3͒ spin chains: ͑1͒ a translationally invariant parent H... more We introduce several exact models for SU͑3͒ spin chains: ͑1͒ a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a threefold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3 of SU͑3͒ if the original spins of the model transform under representation 3. ͑2͒ a family of parent Hamiltonians for valence bond solids of SU͑3͒ chains with spin representations 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement, and a Haldane gap in the excitation spectrum.
Physical Review B, 2009
We identify and investigate the new parameter regime of small charge solitons in one-dimensional ... more We identify and investigate the new parameter regime of small charge solitons in one-dimensional arrays of Josephson junctions. We obtain the dispersion relation of the soliton and show that it unexpectedly flattens in the outer region of the Brillouin zone. We demonstrate Lorentz contraction of the soliton in the middle of the Brillouin zone as well as broadening of the soliton in the flat band regime.
Physical Review B, 2007
To begin with, we introduce several exact models for SU͑3͒ spin chains: First is a translationall... more To begin with, we introduce several exact models for SU͑3͒ spin chains: First is a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a threefold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3 of SU͑3͒ if the original spins of the model transform under representation 3. Second is a family of parent Hamiltonians for valence bond solids of SU͑3͒ chains with spin representations 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement and, hence, a Haldane gap in the excitation spectrum. We generalize some of our models to SU͑n͒. Finally, we use the emerging rules for the construction of valence bond solid states to argue that models of antiferromagnetic chains of SU͑n͒ spins, in general, possess a Haldane gap if the spins transform under a representation corresponding to a Young tableau consisting of a number of boxes which is divisible by n. If and n have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If and n have a common divisor different from n, it will depend on the specifics of the model including the range of the interaction.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2013
Motivated by the recent progress in engineering artificial non-Abelian gauge fields for ultracold... more Motivated by the recent progress in engineering artificial non-Abelian gauge fields for ultracold fermions in optical lattices, we investigate the time-reversal-invariant Hofstadter-Hubbard model. We include an additional staggered lattice potential and an artificial Rashba-type spin-orbit coupling term available in experiment. Without interactions, the system can be either a (semi)-metal, a normal or a topological insulator, and we present the non-Abelian generalization of the Hofstadter butterfly. Using a combination of real-space dynamical mean-field theory (RDMFT), analytical arguments, and Monte-Carlo simulations we study the effect of strong on-site interactions. We determine the interacting phase diagram, and discuss a scenario of an interactioninduced transition from normal to topological insulator. At half-filling and large interactions, the system is described by a quantum spin Hamiltonian, which exhibits exotic magnetic order due to the interplay of Rashba-type spinorbit coupling and the artificial time-reversal-invariant magnetic field term. We determine the magnetic phase diagram: both for the itinerant model using RDMFT and for the corresponding spin model in the classical limit using Monte-Carlo simulations.
Physical Review B, 2010
We systematically study the phase diagram of S = 2 spin chain by means of density-matrix renormal... more We systematically study the phase diagram of S = 2 spin chain by means of density-matrix renormalization group and exact diagonalization. We confirm the presence of a dimer phase in the AKLT-SZH model and find that the whole phase boundary between dimer and SZH phases, including the multicritical point, is a critical line with central charge c = 5/2. Finally, we propose and confirm that this line corresponds to SO(5)1 Wess-Zumino-Witten conformal field theory.
We show that the concept of bipartite fluctuations F provides a very efficient tool to detect qua... more We show that the concept of bipartite fluctuations F provides a very efficient tool to detect quantum phase transitions in strongly correlated systems. Using state of the art numerical techniques complemented with analytical arguments, we investigate paradigmatic examples for both quantum spins and bosons. As compared to the von Neumann entanglement entropy, we observe that F allows to find quantum critical points with a much better accuracy in one dimension. We further demonstrate that F can be successfully applied to the detection of quantum criticality in higher dimensions with no prior knowledge of the universality class of the transition. Promising approaches to experimentally access fluctuations are discussed for quantum antiferromagnets and cold gases.
We introduce several exact models for SU͑3͒ spin chains: ͑1͒ a translationally invariant parent H... more We introduce several exact models for SU͑3͒ spin chains: ͑1͒ a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a threefold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3 of SU͑3͒ if the original spins of the model transform under representation 3. ͑2͒ a family of parent Hamiltonians for valence bond solids of SU͑3͒ chains with spin representations 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement, and a Haldane gap in the excitation spectrum.