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Papers by George Japaridze
Physical Review B, 2016
We explore a scheme for engineering a one-dimensional spinless p-wave superconductor hosting unpa... more We explore a scheme for engineering a one-dimensional spinless p-wave superconductor hosting unpaired Majorana zero-energy modes, using an all-electric setup with a spin-orbit coupled quantum wire in proximity to an s-wave superconductor. The required crossing of the Fermi level by a single spin-split energy band is ensured by employing a periodically modulated Rashba interaction, which, assisted by electron-electron interactions and a uniform Dresselhaus interaction, opens a gap at two of the spin-orbit shifted Fermi points. While an implementation in a hybrid superconductorsemiconductor device requires improvements upon present-day capabilities, a variant of our scheme where spin-orbit-coupled cold fermions are effectively proximity-coupled to a BEC reservoir of Feshbach molecules may provide a ready-to-use platform.
Physical Review B, 2019
We consider a one-dimensional commensurate Peierls insulator in the presence of spin-dependent si... more We consider a one-dimensional commensurate Peierls insulator in the presence of spin-dependent sign-alternating potentials. In a continuum description, the latter supply the fermions with spindependent "relativistic" masses m ↑,↓. The ground-state phase diagram describes three gapped phases: the CDW and SDW-like band insulator phases sandwiched by a "mixed" phase in which the CDW and SDW superstructures coexist with a nonzero spontaneous dimerization (SD). The critical lines separating the massive phases belong to the Ising universality class. The Ising criticality is accompanied by the Kohn anomaly in the renormalized phonon spectrum. We derive a Ginzburg criterion which specifies a narrow region around the critical point where quantum fluctuations play a dominant role, rendering the adiabatic (or mean-field) approximation inapplicable. A full account of quantum effects is achieved in the anti-adiabatic limit where the effective lowenergy theory represents a massive version the N=4 Gross-Neveu model. Using Abelian bosonization we demonstrate that the description of the SD phase, including its critical boundaries, is well approximated by a sum of two effective double-frequency sine-Gordon (DSG) models subject to self-consistency conditions that couple the charge and spin sectors. Using the well-known critical properties of the DSG model we obtain the singular parts of the dimerization order parameter and staggered charge and spin susceptibilities near the Ising critical lines. We show that, in the antiadiabatic limit, on the line m ↓ = 0 there exists of a Berezinskii-Kosterlitz-Thouless critical point separating a Luttinger-liquid gapless phase from the spontaneously dimerized one. We also discuss topological excitations of the model carrying fractional charge and spin.
Physical Review B, 2020
A key concept in the emerging field of spintronics is the electric field control of spin precessi... more A key concept in the emerging field of spintronics is the electric field control of spin precession via the effective magnetic field generated by the Rashba spin orbit interaction (RSOI). Here, by extensive Density Matrix Renormalization Group computations, we demonstrate the presence of alternating spin current order in the gapped phases of a quantum wire with spatially modulated RSOI and repulsive electron-electron interactions. Our results are analytically supported by bosonization and by a mapping to a locally rotated spin basis.
Journal of Magnetism and Magnetic Materials, 2021
We study a one-dimensional spin-1/2 XXZ Heisenberg model with alternating Dzyaloshinskii-Moriya i... more We study a one-dimensional spin-1/2 XXZ Heisenberg model with alternating Dzyaloshinskii-Moriya interaction, using the numerical Lanczos method. Recently, the ground state (GS) phase diagram of this model has been established using the bosonization approach and extensive density matrix renormalization group computations. Four quantum phases-saturated ferromagnetic (FM), Luttinger liquid (LL), and two (C1 and C2) gapped phases with composite structure of GS order, characterized by the coexistence of long-range alternating dimer, chirality and antiferromagnetic order have been identified. Here we reexamine the same problem using the exact diagonalization Lanczos method for chains up to N = 26 sites and explicitly detect positions of quantum critical points (QCP) by investigating the quantum correlations as the entanglement and the quantum discord (QD). It is shown that the entanglement quantified by concurrence and the first derivative of the QD are able to reveal besides the standard FM QCP also the Berezinskii-Kosterlitz-Thouless (BKT) phase transition point between the LL and the gapped C1 phase and the Ising type critical point separating the C1 and C2 phases.
Physical review. E, 2021
We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatial... more We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatially modulated Dzyaloshinskii-Moriya interaction in the presence of an alternating magnetic field applied along the z[over ̂] axis. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of a magnetic field, the ground-state phase diagram of the model includes, besides the ferromagnetic and gapless Luttinger-liquid phases, two gapped phases: the composite (C1) phase characterized by the coexistence of long-range-ordered (LRO) alternating dimerization and spin chirality patterns, and the composite (C2) phase characterized by, in addition to the coexisting spin dimerization and alternating chirality patterns, the presence of LRO antiferromagnetic order. In the case of mentioned composite gapped phases, and in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions from a...
The ground-state magnetic phase diagram of a two-leg spin ladder with trimerized modulated rung e... more The ground-state magnetic phase diagram of a two-leg spin ladder with trimerized modulated rung exchange is studied using the continuum-limit bosonization approach. In the limit where the rung exchange is dominant, the model is mapped onto the effective quantum sine-Gordon model with topological term. Six quantum phase transitions at different critical magnetic fields are identified. We have shown that the magnetization curve of the system exhibits two plateaus at magnetization equal to the 1/3 and 2/3 of the saturation value. The width of the plateaus is proportional to the excitation gap at given magnetization and scales as , where is the amplitude of rung exchange modulation and the critical
The European Physical Journal B, 2019
We study the ground-state magnetic phase diagram of a spin S = 1/2 antiferromagnetic two-leg ladd... more We study the ground-state magnetic phase diagram of a spin S = 1/2 antiferromagnetic two-leg ladder in the presence of period two lattice units modulated, Dzyaloshinskii-Moriya (DM) interaction along the legs. We consider the case of collinear DM vectors and strong rung exchange and magnetic field. In this limit we map the initial ladder model onto the effective spin σ = 1/2 XXZ chain and study the latter using the continuum-limit bosonization approach. We identified four quantum phase transitions and corresponding critical magnetic fields, which mark transitions from the spin gapped regimes into the gapless quantum spin-liquid regimes. In the gapped phases the magnetization curve of the system shows plateaus at magnetisation M = 0 and to its saturation value per rung M = Msat = 1. We have shown that the very presence of alternating DM interaction leads to opening of a gap in the excitation spectrum at magnetization M = 0.5Msat. The width of the magnetization plateau at M = 0.5Msat, is determined by the associated with the dynamical generation of a gap in the spectrum is calculated and is shown that its length scales as (D0D1/J 2) α where D0, D1 are uniform and staggered components of the DM term, J is the intraleg exchange and α ≤ 3/4 and weakly depends on the DM couplings.
Physical Review B, 2017
A repulsive Hubbard model with both spin-asymmetric hopping (t ↑ = t ↓) and a staggered potential... more A repulsive Hubbard model with both spin-asymmetric hopping (t ↑ = t ↓) and a staggered potential (of strength ∆) is studied in one dimension. The model is a compound of the mass-imbalanced (t ↑ = t ↓ , ∆ = 0) and ionic (t ↑ = t ↓ , ∆ > 0) Hubbard models, and may be realized by cold atoms in engineered optical lattices. We use mostly mean-field theory to determine the phases and phase transitions in the ground state for a half-filled band (one particle per site). We find that a period-two modulation of the particle (or charge) density and an alternating spin density coexist for arbitrary Hubbard interaction strength, U 0. The amplitude of the charge modulation is largest at U = 0, decreases with increasing U and tends to zero for U → ∞. The amplitude for spin alternation increases with U and tends to saturation for U → ∞. Charge order dominates below a value Uc, whereas magnetic order dominates above. The mean-field Hamiltonian has two gap parameters, ∆ ↑ and ∆ ↓ , which have to be determined self-consistently. For U < Uc both parameters are positive, for U > Uc they have different signs, and for U = Uc one gap parameter jumps from a positive to a negative value. The weakly first-order phase transition at Uc can be interpreted in terms of an avoided criticality (or metallicity). The system is reluctant to restore a symmetry that has been broken explicitly.
Journal of Mathematical Sciences, 2016
The tight-binding model of quantum particle on a honeycomb lattice is investigated in the presenc... more The tight-binding model of quantum particle on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. The one-particle Hamiltonian is expressed in terms of the generators of the quantum group Uq(sl2). The corresponding Harper equation is rewritten as a system of two coupled functional equations in the complex plane. The system is shown to exhibit certain symmetry that allows one to resolve the entanglement, and the basic single equation determining the eigenvalues and eigenstates is obtained. Equations specifying the roots of eigenstates in the complex plane are found.
Journal of Physics: Condensed Matter, 2007
We study the ground state phase diagram of a two-leg spin ladder with anisotropic ferromagnetic l... more We study the ground state phase diagram of a two-leg spin ladder with anisotropic ferromagnetic leg couplings under the influence of a symmetry breaking transverse magnetic field by the exact diagonalization technique. In the case of antiferromagnetic coupling between legs we identified two phase transitions in the plane of magnetic field vs interchain coupling strength. The first one corresponds to the transition from the gapped rung-singlet phase to the gapped stripe-ferromagnetic phase. The second one represents the transition from the gapped stripe-ferromagnetic phase into the fully polarized ferromagnetic phase.
Physical Review B, 2017
We propose a spin valve device based on the interplay of a modulated spin-orbit interaction and a... more We propose a spin valve device based on the interplay of a modulated spin-orbit interaction and a uniform external magnetic field acting on a quantum wire. Half-metal phases, where electrons with only a selected spin polarization exhibit ballistic conductance, can be tuned by varying the magnetic field. These half-metal phases are proven to be robust against electron-electron repulsive interactions. Our results arise from a combination of explicit band diagonalization, bosonization techniques and extensive DMRG computations.
Bulletin of the American Physical Society, Mar 3, 2015
We explore the possibility of a superconducting proximity effect in a synthetic helical liquid, f... more We explore the possibility of a superconducting proximity effect in a synthetic helical liquid, formed in a quantum wire in the presence of a spatially periodic Rashba interaction [1]. The practicality and robustness of this novel scheme for producing a 1D p-wave superconductor is discussed [2].
ABSTRACT We investigate the ground-state phase diagram of the one-dimensional "ionic&... more ABSTRACT We investigate the ground-state phase diagram of the one-dimensional "ionic" Hubbard model with an alternating periodic potential at half-filling by numerical diagonalization of finite systems with the Lanczos and density matrix renormalization group (DMRG) methods. We identify an insulator-insulator phase transition from a band to a correlated insulator with simultaneous charge and bond-charge order. The transition point is characterized by the vanishing of the optical excitation gap while simultaneously the charge and spin gaps remain finite and equal. Indications for a possible second transition into a Mott-insulator phase are discussed. The analises is extended to the 3/4-filling and alternating Coulomb interaction -- minimum model Hamiltonian for the crossover from the charge-transfer insulator to the Mott insulator.
International Journal of Modern Physics B, 2016
We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubb... more We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubbard model (IHM) with alternating on-site interaction in the limit of strong repulsion. It is shown that the effective Hamiltonian is that of a spin S = 1/2 anisotropic XXZ Heisenberg chain with alternating next-nearest-neighbor (NNN) and three-spin couplings in the presence of a uniform and a staggered magnetic field.
Physics of Condensed Matter
ABSTRACT
Physical Review B, 2016
We explore a scheme for engineering a one-dimensional spinless p-wave superconductor hosting unpa... more We explore a scheme for engineering a one-dimensional spinless p-wave superconductor hosting unpaired Majorana zero-energy modes, using an all-electric setup with a spin-orbit coupled quantum wire in proximity to an s-wave superconductor. The required crossing of the Fermi level by a single spin-split energy band is ensured by employing a periodically modulated Rashba interaction, which, assisted by electron-electron interactions and a uniform Dresselhaus interaction, opens a gap at two of the spin-orbit shifted Fermi points. While an implementation in a hybrid superconductorsemiconductor device requires improvements upon present-day capabilities, a variant of our scheme where spin-orbit-coupled cold fermions are effectively proximity-coupled to a BEC reservoir of Feshbach molecules may provide a ready-to-use platform.
Physical Review B, 2019
We consider a one-dimensional commensurate Peierls insulator in the presence of spin-dependent si... more We consider a one-dimensional commensurate Peierls insulator in the presence of spin-dependent sign-alternating potentials. In a continuum description, the latter supply the fermions with spindependent "relativistic" masses m ↑,↓. The ground-state phase diagram describes three gapped phases: the CDW and SDW-like band insulator phases sandwiched by a "mixed" phase in which the CDW and SDW superstructures coexist with a nonzero spontaneous dimerization (SD). The critical lines separating the massive phases belong to the Ising universality class. The Ising criticality is accompanied by the Kohn anomaly in the renormalized phonon spectrum. We derive a Ginzburg criterion which specifies a narrow region around the critical point where quantum fluctuations play a dominant role, rendering the adiabatic (or mean-field) approximation inapplicable. A full account of quantum effects is achieved in the anti-adiabatic limit where the effective lowenergy theory represents a massive version the N=4 Gross-Neveu model. Using Abelian bosonization we demonstrate that the description of the SD phase, including its critical boundaries, is well approximated by a sum of two effective double-frequency sine-Gordon (DSG) models subject to self-consistency conditions that couple the charge and spin sectors. Using the well-known critical properties of the DSG model we obtain the singular parts of the dimerization order parameter and staggered charge and spin susceptibilities near the Ising critical lines. We show that, in the antiadiabatic limit, on the line m ↓ = 0 there exists of a Berezinskii-Kosterlitz-Thouless critical point separating a Luttinger-liquid gapless phase from the spontaneously dimerized one. We also discuss topological excitations of the model carrying fractional charge and spin.
Physical Review B, 2020
A key concept in the emerging field of spintronics is the electric field control of spin precessi... more A key concept in the emerging field of spintronics is the electric field control of spin precession via the effective magnetic field generated by the Rashba spin orbit interaction (RSOI). Here, by extensive Density Matrix Renormalization Group computations, we demonstrate the presence of alternating spin current order in the gapped phases of a quantum wire with spatially modulated RSOI and repulsive electron-electron interactions. Our results are analytically supported by bosonization and by a mapping to a locally rotated spin basis.
Journal of Magnetism and Magnetic Materials, 2021
We study a one-dimensional spin-1/2 XXZ Heisenberg model with alternating Dzyaloshinskii-Moriya i... more We study a one-dimensional spin-1/2 XXZ Heisenberg model with alternating Dzyaloshinskii-Moriya interaction, using the numerical Lanczos method. Recently, the ground state (GS) phase diagram of this model has been established using the bosonization approach and extensive density matrix renormalization group computations. Four quantum phases-saturated ferromagnetic (FM), Luttinger liquid (LL), and two (C1 and C2) gapped phases with composite structure of GS order, characterized by the coexistence of long-range alternating dimer, chirality and antiferromagnetic order have been identified. Here we reexamine the same problem using the exact diagonalization Lanczos method for chains up to N = 26 sites and explicitly detect positions of quantum critical points (QCP) by investigating the quantum correlations as the entanglement and the quantum discord (QD). It is shown that the entanglement quantified by concurrence and the first derivative of the QD are able to reveal besides the standard FM QCP also the Berezinskii-Kosterlitz-Thouless (BKT) phase transition point between the LL and the gapped C1 phase and the Ising type critical point separating the C1 and C2 phases.
Physical review. E, 2021
We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatial... more We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatially modulated Dzyaloshinskii-Moriya interaction in the presence of an alternating magnetic field applied along the z[over ̂] axis. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of a magnetic field, the ground-state phase diagram of the model includes, besides the ferromagnetic and gapless Luttinger-liquid phases, two gapped phases: the composite (C1) phase characterized by the coexistence of long-range-ordered (LRO) alternating dimerization and spin chirality patterns, and the composite (C2) phase characterized by, in addition to the coexisting spin dimerization and alternating chirality patterns, the presence of LRO antiferromagnetic order. In the case of mentioned composite gapped phases, and in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions from a...
The ground-state magnetic phase diagram of a two-leg spin ladder with trimerized modulated rung e... more The ground-state magnetic phase diagram of a two-leg spin ladder with trimerized modulated rung exchange is studied using the continuum-limit bosonization approach. In the limit where the rung exchange is dominant, the model is mapped onto the effective quantum sine-Gordon model with topological term. Six quantum phase transitions at different critical magnetic fields are identified. We have shown that the magnetization curve of the system exhibits two plateaus at magnetization equal to the 1/3 and 2/3 of the saturation value. The width of the plateaus is proportional to the excitation gap at given magnetization and scales as , where is the amplitude of rung exchange modulation and the critical
The European Physical Journal B, 2019
We study the ground-state magnetic phase diagram of a spin S = 1/2 antiferromagnetic two-leg ladd... more We study the ground-state magnetic phase diagram of a spin S = 1/2 antiferromagnetic two-leg ladder in the presence of period two lattice units modulated, Dzyaloshinskii-Moriya (DM) interaction along the legs. We consider the case of collinear DM vectors and strong rung exchange and magnetic field. In this limit we map the initial ladder model onto the effective spin σ = 1/2 XXZ chain and study the latter using the continuum-limit bosonization approach. We identified four quantum phase transitions and corresponding critical magnetic fields, which mark transitions from the spin gapped regimes into the gapless quantum spin-liquid regimes. In the gapped phases the magnetization curve of the system shows plateaus at magnetisation M = 0 and to its saturation value per rung M = Msat = 1. We have shown that the very presence of alternating DM interaction leads to opening of a gap in the excitation spectrum at magnetization M = 0.5Msat. The width of the magnetization plateau at M = 0.5Msat, is determined by the associated with the dynamical generation of a gap in the spectrum is calculated and is shown that its length scales as (D0D1/J 2) α where D0, D1 are uniform and staggered components of the DM term, J is the intraleg exchange and α ≤ 3/4 and weakly depends on the DM couplings.
Physical Review B, 2017
A repulsive Hubbard model with both spin-asymmetric hopping (t ↑ = t ↓) and a staggered potential... more A repulsive Hubbard model with both spin-asymmetric hopping (t ↑ = t ↓) and a staggered potential (of strength ∆) is studied in one dimension. The model is a compound of the mass-imbalanced (t ↑ = t ↓ , ∆ = 0) and ionic (t ↑ = t ↓ , ∆ > 0) Hubbard models, and may be realized by cold atoms in engineered optical lattices. We use mostly mean-field theory to determine the phases and phase transitions in the ground state for a half-filled band (one particle per site). We find that a period-two modulation of the particle (or charge) density and an alternating spin density coexist for arbitrary Hubbard interaction strength, U 0. The amplitude of the charge modulation is largest at U = 0, decreases with increasing U and tends to zero for U → ∞. The amplitude for spin alternation increases with U and tends to saturation for U → ∞. Charge order dominates below a value Uc, whereas magnetic order dominates above. The mean-field Hamiltonian has two gap parameters, ∆ ↑ and ∆ ↓ , which have to be determined self-consistently. For U < Uc both parameters are positive, for U > Uc they have different signs, and for U = Uc one gap parameter jumps from a positive to a negative value. The weakly first-order phase transition at Uc can be interpreted in terms of an avoided criticality (or metallicity). The system is reluctant to restore a symmetry that has been broken explicitly.
Journal of Mathematical Sciences, 2016
The tight-binding model of quantum particle on a honeycomb lattice is investigated in the presenc... more The tight-binding model of quantum particle on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. The one-particle Hamiltonian is expressed in terms of the generators of the quantum group Uq(sl2). The corresponding Harper equation is rewritten as a system of two coupled functional equations in the complex plane. The system is shown to exhibit certain symmetry that allows one to resolve the entanglement, and the basic single equation determining the eigenvalues and eigenstates is obtained. Equations specifying the roots of eigenstates in the complex plane are found.
Journal of Physics: Condensed Matter, 2007
We study the ground state phase diagram of a two-leg spin ladder with anisotropic ferromagnetic l... more We study the ground state phase diagram of a two-leg spin ladder with anisotropic ferromagnetic leg couplings under the influence of a symmetry breaking transverse magnetic field by the exact diagonalization technique. In the case of antiferromagnetic coupling between legs we identified two phase transitions in the plane of magnetic field vs interchain coupling strength. The first one corresponds to the transition from the gapped rung-singlet phase to the gapped stripe-ferromagnetic phase. The second one represents the transition from the gapped stripe-ferromagnetic phase into the fully polarized ferromagnetic phase.
Physical Review B, 2017
We propose a spin valve device based on the interplay of a modulated spin-orbit interaction and a... more We propose a spin valve device based on the interplay of a modulated spin-orbit interaction and a uniform external magnetic field acting on a quantum wire. Half-metal phases, where electrons with only a selected spin polarization exhibit ballistic conductance, can be tuned by varying the magnetic field. These half-metal phases are proven to be robust against electron-electron repulsive interactions. Our results arise from a combination of explicit band diagonalization, bosonization techniques and extensive DMRG computations.
Bulletin of the American Physical Society, Mar 3, 2015
We explore the possibility of a superconducting proximity effect in a synthetic helical liquid, f... more We explore the possibility of a superconducting proximity effect in a synthetic helical liquid, formed in a quantum wire in the presence of a spatially periodic Rashba interaction [1]. The practicality and robustness of this novel scheme for producing a 1D p-wave superconductor is discussed [2].
ABSTRACT We investigate the ground-state phase diagram of the one-dimensional "ionic&... more ABSTRACT We investigate the ground-state phase diagram of the one-dimensional "ionic" Hubbard model with an alternating periodic potential at half-filling by numerical diagonalization of finite systems with the Lanczos and density matrix renormalization group (DMRG) methods. We identify an insulator-insulator phase transition from a band to a correlated insulator with simultaneous charge and bond-charge order. The transition point is characterized by the vanishing of the optical excitation gap while simultaneously the charge and spin gaps remain finite and equal. Indications for a possible second transition into a Mott-insulator phase are discussed. The analises is extended to the 3/4-filling and alternating Coulomb interaction -- minimum model Hamiltonian for the crossover from the charge-transfer insulator to the Mott insulator.
International Journal of Modern Physics B, 2016
We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubb... more We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubbard model (IHM) with alternating on-site interaction in the limit of strong repulsion. It is shown that the effective Hamiltonian is that of a spin S = 1/2 anisotropic XXZ Heisenberg chain with alternating next-nearest-neighbor (NNN) and three-spin couplings in the presence of a uniform and a staggered magnetic field.
Physics of Condensed Matter
ABSTRACT