arXiv subjects

G. I. Japaridze

Publications and source records attributed to G. I. Japaridze.

At least 19 recordsLinked to original sources

arXiv2026

Critical Phases of the extended isotropic $XY$ chain with four-spin interaction

Using the Jordan-Wigner transformation we calculate exactly the ground state and low-temperature thermodynamic properties of the spin $S=1/2$ isotropic $XX$ chain with four spin interaction. In terms of the equivalent spinless fermion (SF) representation the system is viewed as a lattice fermion gas with nearest-neighbor ($J$) and next-next-next-neighbor ($J^{\ast}/4$) hopping. It is shown that with the increase of four spin coupling, at $J^{\ast}_{c} = 4J/3$ the system experiences the Lifshitz type topological phase transition characterized by the tripling of Fermi points. The quantum phase transition (QPT) point marks transition from a gapless spin-liquid phase of standard $XX$ chain into again a gapless spin-liquid phase with different character of power-low decay of spin correlations. At the transition point the free fermion dispersion relation shows flattering at Fermi points, what determines singular character of density of states $ρ(ω)\sim (ω/J)^{-2/3}$ and as a consequence unconventional temperature dependence of heat capacity of the system $C\sim (T/J^{\ast})^{1/3}$, and singular magnetic susceptibility of the system $χ(H)\sim (H/J^{\ast})^{-2/3}$. In the case of alternating magnetic field the system is characterized by the rich ground state phase diagram which contains fully polarized (ferromagnetic), gapped antiferromagnetic (AFM) and spin liquid phases. At the transition point from the gapped AFM phase into the gapless polarized spin liquid phase the system shows rapid increase of magnetization $m\sim(H-H_c)^{1/6}$ and magnetic susceptibility a singular behavior as $χ(H)\sim (H-H_c)^{-5/6}$.

cond-mat.str-el↗

arXiv2024

Orbital antiferromagnetic currents in a frustrated fermionic ladder

We consider a spinless $t$-$t'$ ionic Hubbard chain at 1/2 filling and large hopping ratio $t'/t$. In this limit the model adequately maps onto a weakly coupled triangular ladder with a potential interchain bias. The low-energy properties of the system are formed due to the interplay of geometrical frustration, correlations and charge imbalance. We derive the effective field-theoretical model to study universal properties of the model in the scaling limit. We show that at full dynamical frustration the ground state of the ladder represents a repulsive version of the Luther-Emery liquid with dominant orbital antiferromagnetic correlations exhibiting the slowest power-law decay in the ground state. Pairing correlations also display algebraic order but are subdominant. At an incomplete dynamical frustration a finite commensurability gap is dynamically generated, and the fluctuating OAF transforms to a long-range ordered state with a spontaneously broken time reversal symmetry. The mass gap in the spectrum of relative density fluctuations gets suppressed upon increasing the potential bias.

cond-mat.str-el↗

arXiv2021

Magnetic phase diagram of a spin-1/2 XXZ chain with modulated Dzyaloshinskii-Moriya interaction

We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with spatially modulated Dzyaloshinskii-Moriya interaction in the presence of applied along with the $\hat{z}$ axis alternating magnetic field. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of the magnetic field, the ground-state phase diagram of the model includes besides the ferromagnetic and gapless Luttiger-Liquid (LL) phases two gapped phases, the composite (C1) phase characterized by the coexistence of the long-range-ordered (LRO) alternating dimerization and the spin chirality patterns, and the composite (C2) phase characterized in addition to the coexisting spin dimerization and alternating chirality patterns, by the presence of LRO antiferromagnetic order. In the case of two-letter gapped phases, in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions (QPT) from a gapful phase into the gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalizations studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of the staggered component of the magnetic field vapes out the composite (C1) in favour of the composite gapped (C2) phase.

cond-mat.str-el↗

arXiv2020

Quantum correlations in the spin-1/2 Heisenberg XXZ chain with modulated Dzyaloshinskii-Moriya interaction

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.

cond-mat.str-el↗

arXiv2020

Long range alternating spin current order in a quantum wire with modulated spin-orbit interactions

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.

cond-mat.str-el↗

arXiv2019

Long-range spin chirality dimer order in the Heisenberg chain with modulated Dzyaloshinskii-Moriya interactions

The ground state phase diagram of a spin $S=1/2$ $XXZ$ Heisenberg chain with spatially modulated Dzyaloshinskii-Moriya (DM) interaction $ {\cal H}= \sum_n J\left[\left(S^x_n S^x_{n+1} +S^y_n S^y_{n+1}+ΔS^z_n S^z_{n+1}\right)+(D_0+(-1)^n D_1)\left(S^x_n S^y_{n+1} -S^y_n S^{x}_{n+1} \right) \right] $ is studied using the continuum-limit bosonization approach and extensive density matrix renormalization group computations. It is shown that the effective continuum-limit bosonized theory of the model is given by the double frequency sine-Gordon model (DSG) where the frequences i.e. the scaling dimensions of the two competing cosine perturbation terms depend on the effective anisotropy parameter $γ^*=JΔ/\sqrt{J^2+D_0^2+D_1^2}$. Exploring the ground state properties of the DSG model we have shown that the zero-temperature phase diagram contains the following four phases: (i) the ferromagnetic phase at $γ^*<-1$; (ii) the gapless Luttinger-liquid (LL) phase at $-1<γ^*< γ^*_{c1}=-1/\sqrt{2}$; (iii) the gapped composite (C1) phase characterized by coexistence of the long-range-ordered (LRO) dimerization pattern $ε\sim (-1)^n (S_n S_{n+1})$ with the LRO alternating spin chirality pattern $κ\sim (-1)^{n}\left(S^{x}_{n}S^{y}_{n+1} -S^{y}_{n}S^{x}_{n+1} \right)$ at $γ^{\ast}_{c1}<γ^{\ast} <γ^{\ast}_{c2}$; and (iv) at $γ^{\ast} >γ^{\ast}_{c2}>1$ the gapped composite (C2) phase characterized in addition to the coexisting spin dimerization and alternating chirality patterns, by the presence of LRO antiferromagnetic order. The transition from the LL to the C1 phase at $γ^*_{c1}$ belongs to the Berezinskii-Kosterlitz-Thouless universality class, while the transition at $γ^*_{c2}$ from C1 to C2 phase is of the Ising type.

cond-mat.str-el↗

arXiv2017

Half-metal phases in a quantum wire with modulated spin-orbit interaction

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.

cond-mat.str-el↗

arXiv2016

Synthesizing Majorana zero-energy modes in a periodically gated quantum wire

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 superconductor-semiconductor 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.

cond-mat.str-el↗

arXiv2014

Ultracold fermions in a one-dimensional bipartite optical lattice: metal-insulator transitions driven by shaking

We describe the behavior of a system of fermionic atoms loaded in a bipartite one-dimensional optical lattice that is under the action of an external time-periodic driving force. By using Floquet theory, an effective model with renormalized hopping coefficients is derived. The insulating behavior characterizing the system at half-filling in the absence of driving is dynamically suppressed and for particular values of the driving parameter the system becomes either a standard metal or an unconventional metal with four Fermi points. We use the bosonization technique to investigate the effect of on-site Hubbard interactions on the four Fermi-point metal-insulator phase transition. Attractive interactions are expected to enlarge the regime of parameters where the unconventional metallic phase arises, whereas repulsive interactions reduce it. This metallic phase is known to be a Luther-Emery liquid (spin gapped metal) for both, repulsive and attractive interactions, contrarily to the usual Hubbard model which exhibits a Mott insulator phase for repulsive interactions. Ultracold fermions in driven one-dimensional bipartite optical lattices provide an interesting platform for the realization of this long studied four Fermi-point unconventional metal.

cond-mat.quant-gas↗

arXiv2014

Quantum simulation of correlated-hopping models with fermions in optical lattices

By using a modulated magnetic field in a Feshbach resonance for ultracold fermionic atoms in optical lattices, we show that it is possible to engineer a class of models usually referred to as correlated-hopping models. These models differ from the Hubbard model in exhibiting additional density-dependent interaction terms that affect the hopping processes. In addition to the spin-SU(2) symmetry, they also possess a charge-SU(2) symmetry, which opens the possibility of investigating the $η$-pairing mechanism for superconductivity introduced by Yang for the Hubbard model. We discuss the known solution of the model in 1D (where $η$ states have been found in the degenerate manifold of the ground state) and show that, away from the integrable point, quantum Monte Carlo simulations at half filling predict the emergence of a phase with coexisting incommensurate spin and charge order.

cond-mat.quant-gas↗

arXiv2014

Edge states in 2D lattices with hopping anisotropy and Chebyshev polynomials

Analytic technique based on Chebyshev polynomials is developed for studying two-dimensional lattice ribbons with hopping anisotropy. In particular, the tight-binding models on square and triangle lattice ribbons are investigated with anisotropic nearest neighbouring hoppings. For special values of hopping parameters the square lattice becomes topologically equivalent to a honeycomb one either with zigzag or armchair edges. In those cases as well as for triangle lattices we perform the exact analytic diagonalization of tight-binding Hamiltonians in terms of Chebyshev polynomials. Deep inside the edge state subband the wave functions exhibit exponential spatial damping which turns into power-law damping at edge-bulk transition point. It is shown that strong hopping anisotropy crashes down edge states, and the corresponding critical conditions are found.

math-ph↗

arXiv2013

Magnetic-field switchable metal-insulator transitions in a quasi-helical conductor

We study Anderson localization in disordered helical conductors that are obtained from one-dimensional conductors with spin-orbit interaction and a magnetic field, or from equivalent systems. We call such conductors "quasi-helical" because the spins of the counterpropagating modes are not perfectly antiparallel and have a small spin-wavefunction overlap that is tunable by the magnetic field. Due to the overlap, disorder backscattering is possible and allows a localization transition. A conductor can pass through two localization transitions with increasing field, one from the conventionally localized system to the quasi-helical conductor (with localization length exceeding the system length), and one at a higher field again to a localized state, due now, however, to backscattering below the magnetic field induced pseudo-gap. We investigate these transitions using a unified two-step renormalization group approach.

cond-mat.mes-hall↗

arXiv2012

Magnetic properties of the spin $S=1/2$ Heisenberg chain with hexamer modulation of exchange

We consider the spin-1/2 Heisenberg chain with alternating spin exchange %on even and odd sites in the presence of additional modulation of exchange on odd bonds with period three. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective $XXZ$ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped string order into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to 1/3 and 2/3 of the saturation value. These phases reveal themselves also in magnetization curve as plateaus at corresponding values of magnetization. As the result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.

cond-mat.str-el↗

arXiv2012

Magnetic phase diagram of the dimerized spin $S=1/2$ ladder

The ground-state magnetic phase diagram of a spin $S=1/2$ two-leg ladder with alternating rung exchange $J_{\perp}(n)=J_{\perp}[1 + (-1)^{n} δ]$ is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sine-Gordon model with topological term and identified two quantum phase transitions at magnetization equal to the half of saturation value from a gapped to the gapless regime. These quantum transitions belong to the universality class of the commensurate-incommensurate phase transition. We have also shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. We also present a detailed numerical analysis of the low energy excitation spectrum and the ground state magnetic phase diagram of the ladder with rung-exchange alternation using Lanczos method of numerical diagonalizations for ladders with number of sites up to N=28. We have calculated numerically the magnetic field dependence of the low-energy excitation spectrum, magnetization and the on-rung spin-spin correlation function. We have also calculated the width of the magnetization plateau and show that it scales as $δ^ν$, where critical exponent varies from $ν=0.87\pm0.01$ in the case of a ladder with isotropic antiferromagnetic legs to $ν=1.82\pm0.01 $ in the case of ladder with ferromagnetic legs. Obtained numerical results are in an complete agreement with estimations made within the continuum-limit approach.

cond-mat.str-el↗

arXiv2011

Modulated Rashba interaction in a quantum wire: Spin and charge dynamics

It was recently shown that a spatially modulated Rashba spin-orbit coupling in a quantum wire drives a transition from a metallic to an insulating state when the wave number of the modulation becomes commensurate with the Fermi wave length of the electrons in the wire. It was suggested that the effect may be put to practical use in a future spin transistor design. In the present article we revisit the problem and present a detailed analysis of the underlying physics. First, we explore how the build-up of charge density wave correlations in the quantum wire due to the periodic gate configuration that produces the Rashba modulation influences the transition to the insulating state. The interplay between the modulations of the charge density and that of the spin-orbit coupling turns out to be quite subtle: Depending on the relative phase between the two modulations, the joint action of the Rashba interaction and charge density wave correlations may either enhance or reduce the Rashba current blockade effect. Secondly, we inquire about the role of the Dresselhaus spin-orbit coupling that is generically present in a quantum wire embedded in semiconductor heterostructure. While the Dresselhaus coupling is found to work against the current blockade of the insulating state, the effect is small in most materials. Using an effective field theory approach, we also carry out an analysis of effects from electron- electron interactions, and show how the single-particle gap in the insulating state can be extracted from the more easily accessible collective charge and spin excitation thresholds. The smallness of the single-particle gap together with the anti-phase relation between the Rashba and chemical potential modulations pose serious difficulties for realizing a Rashba-controlled current switch in an InAs-based device. Some alternative designs are discussed.

cond-mat.str-el↗

arXiv2011

Quantum criticality of vanadium chains with strong relativistic spin-orbit interaction

We study quantum phase transitions induced by the on-site spin-orbit interaction lambda(L.S) in a toy model of vanadium chains. In the lambda->0 limit, the decoupled spin and orbital sectors are described by a Haldane and an Ising chain, respectively. The gapped ground state is composed of a ferro-orbital order and a spin liquid with finite correlation lengths. In the opposite limit, strong spin-orbital entanglement results in a simultaneous spin and orbital-moment ordering, which can be viewed as an orbital liquid. Using a combination of analytical arguments and density-matrix renormalization group calculation, we show that an intermediate phase, where the ferro-orbital state is accompanied by a spin Neel order, is bounded on both sides by Ising transition lines. Implications for vanadium compounds CaV2O4 and ZnV2O4 are also discussed.

cond-mat.str-el↗

arXiv2010

Edge Dynamics in a Quantum Spin Hall State: Effects from Rashba Spin-Orbit Interaction

We analyze the dynamics of the helical edge modes of a quantum spin Hall state in the presence of a spatially non-uniform Rashba spin-orbit (SO) interaction. A randomly fluctuating Rashba SO coupling is found to open a scattering channel which causes localization of the edge modes for a weakly screened electron-electron (e-e) interaction. A periodic modulation of the SO coupling, with a wave number commensurate with the Fermi momentum, makes the edge insulating already at intermediate strengths of the e-e interaction. We discuss implications for experiments on edge state transport in a HgTe quantum well.

cond-mat.mes-hall↗

arXiv2009

Metal-insulator transition in a quantum wire driven by a modulated Rashba spin-orbit coupling

We study the ground-state properties of electrons confined to a quantum wire and subject to a smoothly modulated Rashba spin-orbit coupling. When the period of the modulation becomes commensurate with the band filling, the Rashba coupling drives a quantum phase transition to a nonmagnetic insulating state. Using bosonization and a perturbative renormalization group approach, we find that this state is robust against electron-electron interactions. The gaps to charge- and spin excitations scale with the amplitude of the Rashba modulation with a common interaction-dependent exponent. An estimate of the expected size of the charge gap, using data for a gated InAs heterostructure, suggests that the effect can be put to practical use in a future spin transistor design.

cond-mat.mes-hall↗