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George I. Japaridze

Publications and source records attributed to George I. Japaridze.

12 recordsLinked to original sources
arXiv2025

The large $|U|$ expansion for a half-filled asymmetric Hubbard model on a triangular ladder in the presence of spin-dependent magnetic flux

We consider a half-filled system of spin-1/2 fermions on a triangular ladder with spin-dependent hopping in the presence of spin-dependent flux. Using the Schrieffer-Wolff transformation, we derive an effective spin Hamiltonian describing the infrared properties of the system in the limit of strong on-site repulsion. The expansion is performed up to the third order in the hopping amplitude over on-site interaction energy. It is shown that the low-energy spin excitations are described by an anisotropic $XXZ$ Heisenberg model with Dzyaloshinskii-Moriya interaction and an unconventional three-spin (correlated exchange) term in the presence of an extended magnetic field. The latter couples not only to $z$-projection of the total spin on a triangular plaquette but also to the product of $z$-components of three spins located on vertices of the triangle. In the case of strong attractive interaction, the corresponding effective model is derived from the repulsive one using the one-spin-component particle-hole transformation. The effective Hamiltonian is given by the same $XXZ$ Heisenberg model, as in the repulsive case, but in terms of pseudospin (charge) operators.

cond-mat.str-el↗
arXiv2023

Repulsion driven metallic phase in the ground state of the half-filled $t-t^{\prime}$ ionic Hubbard chain

An unusual metallic phase is proven to develop in the one dimensional ionic Hubbard model, at half-filling and zero magnetization, at intermediate electron-electron repulsion $U$ when second neighbors hopping is allowed and tuned close to a topological Lifshitz transition (connected with a change of the Fermi surface in the non-interacting system). The metallic state lies between a band insulator phase at low repulsion and a correlated (Mott-like) insulator phase at high repulsion. In approaching the later, the metal supports spontaneous bond charge dimerization and antiferromagnetic correlations. The ground state of the system, attainable by cold atoms in optical lattices for a wide range of the parameter $U$, is extensively explored by numerically exact density-matrix renormalization-group (DMRG) calculations. A combination of mean field and effective field theory (bosonization) provides an analytical understanding of the physical processes underlying the observed phase transitions.

cond-mat.str-el↗
arXiv2022

Mean-field ground-state phase diagram of the ${t-t^\prime}$ ionic-Hubbard chain

Ground state (GS) phase diagram of the one dimensional repulsive Hubbard model with both nearest neighbor ($t$) and next-nearest-neighbor ($t^{\prime}$) hopping and a staggered potential ($Δ$) is determined in the case of half-filled band and zero net magnetization within the mean-field theory. The model may be realized by cold atoms in engineered optical lattices. Connection between the peculiarities of the GS phase diagram of the interacting system and the topological Lifshitz transition in GS of free particle chain is discussed. The mean-field Hamiltonian is given by six order parameters, which are determined self-consistently. It is shown that the GS phase diagram {\em predominantly} consists of insulating phases characterized by coexistence of the long-range ordered modulations of the charge- (I) and antiferromagnetic (AF) spin-density with wavelengths equal to two and/or four lattice units. Below the Lifshitz transition, the GS phase diagram is qualitatively similar to that of the standard (${t^{\prime}=0}$) ionic Hubbard model. After the Lifshitz transition, charge- and spin-density modulations emerge within the sublattices and have wavelengths equal to four lattice units. For moderate values of the on-site repulsion the insulating phases are characterized by the presence of I and AF modulations coexisting with ferrimagnetic spin- and charge-density modulations within the one sublattice, or by the coexistence of I order and additional AF spin density modulation only within the sublattice with high ionic potential. At large repulsion the insulating phase with AF order inside both sublattices and remaining small ionicity left between the sublattices is realized.

cond-mat.str-el↗
arXiv2019

Magnetic phase diagram of a spin S=1/2 antiferromagnetic two-leg ladder in the presence of modulated along legs Dzyaloshinskii-Moriya interaction

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=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=0.5. The width of the magnetization plateau at M=0.5, 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 $(D_{0}D_{1}/J^{2})^α$ where $D_{0},D_{1}$ are uniform and staggered components of the DM term, $J$ is the intraleg exchange and $α\leq 3/4$ and weakly depends on the DM couplings.

cond-mat.str-el↗
arXiv2017

Mass-Imbalanced Ionic Hubbard Chain

A repulsive Hubbard model with both spin-asymmetric hopping (${t_\uparrow\neq t_\downarrow}$) and a staggered potential (of strength $Δ$) is studied in one dimension. The model is a compound of the mass-imbalanced (${t_\uparrow\neq t_\downarrow}$, ${Δ=0}$) and ionic (${t_\uparrow = t_\downarrow}$, ${Δ>0}$) 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, ${U\geqslant 0}$. The amplitude of the charge modulation is largest at ${U=0}$, decreases with increasing $U$ and tends to zero for ${U\rightarrow\infty}$. The amplitude for spin alternation increases with $U$ and tends to saturation for ${U\rightarrow\infty}$. Charge order dominates below a critical value $U_c$, whereas magnetic order dominates above. The mean-field Hamiltonian has two gap parameters, $Δ_\uparrow$ and $Δ_\downarrow$, which have to be determined self-consistently. For ${U U_c}$ they have different signs, and for ${U=U_c}$ one gap parameter jumps from a positive to a negative value. The weakly first-order phase transition at $U_c$ can be interpreted in terms of an avoided criticality (or metallicity). The system is reluctant to restore a symmetry that has been broken explicitly.

cond-mat.str-el↗
arXiv2016

Effective Hamiltonian for a Half-filled Asymmetric Ionic Hubbard Chain with Alternating On-site Interaction

We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubbard model 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 and three-spin couplings in the presence of a uniform and a staggered magnetic field.

cond-mat.str-el↗
arXiv2014

Synthetic helical liquid in a quantum wire

We show that the combination of a Dresselhaus interaction and a spatially periodic Rashba interaction leads to the formation of a helical liquid in a quantum wire when the electron-electron interaction is weakly screened. The effect is sustained by a helicity-dependent effective band gap which depends on the size of the Dresselhaus and Rashba spin-orbit couplings. We propose a design for a semiconductor device in which the helical liquid can be realized and probed experimentally.

cond-mat.str-el↗
arXiv2012

The quantum group, Harper equation and the structure of Bloch eigenstates on a honeycomb lattice

The tight-binding model of quantum particles on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. Provided the magnetic flux per unit hexagon is rational of the elementary flux, the one-particle Hamiltonian is expressed in terms of the generators of the quantum group $U_q(sl_2)$. Employing the functional representation of the quantum group $U_q(sl_2)$ the Harper equation is rewritten as a systems of two coupled functional equations in the complex plane. For the special values of quasi-momentum the entangled system admits solutions in terms of polynomials. The system is shown to exhibit certain symmetry allowing to resolve the entanglement, and basic single equation determining the eigenvalues and eigenstates (polynomials) is obtained. Equations specifying locations of the roots of polynomials in the complex plane are found. Employing numerical analysis the roots of polynomials corresponding to different eigenstates are solved out and the diagrams exhibiting the ordered structure of one-particle eigenstates are depicted.

cond-mat.mes-hall↗
arXiv2012

Quantum phase transition in a dimerized chain with hexamer distortion

We consider the dimerized spin-1/2 Heisenberg chain with spin hexameric distortion of the exchange pattern and study the zero-temperature phase diagram in the parameter space $(J_{1}, J_{2}, J_{3})$ by continuum-limit bosonization approach and the exact diagonalization method. The phase diagram is rich and has two gaped dimer phases. We obtain an estimate of the critical line separating the different gapped dimer phases by the bosonization approach. The existence of the transition line and the difference between dimer phases is checked numerically. The behavior of the energy gap and the dimer order parameter supports the exact location of the gapless line.

cond-mat.str-el↗
arXiv2010

Spin-selective Peierls transition in interacting one-dimensional conductors with spin-orbit interaction

Interacting one-dimensional conductors with Rashba spin-orbit coupling are shown to exhibit a spin-selective Peierls-type transition into a mixed spin-charge-density-wave state. The transition leads to a gap for one-half of the conducting modes, which is strongly enhanced by electron-electron interactions. The other half of the modes remains in a strongly renormalized gapless state and conducts opposite spins in opposite directions, thus providing a perfect spin filter. The transition is driven by magnetic field and by spin-orbit interactions. As an example we show for semiconducting quantum wires and carbon nanotubes that the gap induced by weak magnetic fields or intrinsic spin-orbit interactions can get renormalized by 1 order of magnitude up to 10 - 30 K.

cond-mat.mes-hall↗
arXiv2010

Spin-filtering by field dependent resonant tunneling

We consider theoretically transport in a spinfull one-channel interacting quantum wire placed in an external magnetic field. For the case of two point-like impurities embedded in the wire, under a small voltage bias the spin-polarized current occurs at special points in the parameter space, tunable by a single parameter. At sufficiently low temperatures complete spin-polarization may be achieved, provided repulsive interaction between electrons is not too strong.

cond-mat.str-el↗