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Janusz Jedrzejewski

Publications and source records attributed to Janusz Jedrzejewski.

12 recordsLinked to original sources
arXiv2013

Quantum critical scaling of fidelity in BCS-like model

We study scaling of the ground-state fidelity in neighborhoods of quantum critical points in a model of interacting spinfull fermions - a BCS-like model. Due to the exact diagonalizability of the model, in one and higher dimensions, scaling of the ground-state fidelity can be analyzed numerically with great accuracy, not only for small systems but also for macroscopic ones, together with the crossover region between them. Additionally, in one-dimensional case we have been able to derive a number of analytical formulae for fidelity and show that they accurately fit our numerical results; these results are reported in the article. Besides regular critical points and their neighborhoods, where well-known scaling laws are obeyed, there is the multi-critical point and critical points in its proximity where anomalous scaling behavior is found. We consider also scaling of fidelity in neighborhoods of critical points where fidelity oscillates strongly as the system size or the chemical potential is varied. Our results for a one-dimensional version of a BCS-like model are compared with those obtained by Rams and Damski in similar studies of a quantum spin chain - an anisotropic XY model in transverse magnetic field.

cond-mat.stat-mech↗
arXiv2010

Estimating the Hubbard repulsion sufficient for the onset of nearly-flat-band ferromagnetism

We consider nearly-flat-band Hubbard models of a ferromagnet, that is the models that are weak perturbations of those flat-band Hubbard models whose ground state is ferromagnetic for any nonzero strength $U$ of the Hubbard repulsion. In contrast to the flat-band case, in the nearly-flat-band case the ground state, being paramagnetic for $U$ in a vicinity of zero, turns into a ferromagnetic one only if $U$ exceeds some nonzero threshold value $U_{th}$. We address the question whether $U_{th}$ of the considered models is in a physical range, therefore we attempt at obtaining possibly good estimates of the threshold value $U_{th}$. A rigorous method proposed by Tasaki is extended and the resulting estimates are compared with small-system, finite-size scaling results obtained for open- and periodic-boundary conditions. Contrary to suggestions in literature, we find the latter conditions particularly useful for our task.

cond-mat.str-el↗
arXiv2009

On the nature of striped phases: Striped phases as a stage of "melting" of 2D crystals

We discuss striped phases as a state of matter intermediate between two extreme states: a crystalline state and a segregated state. We argue that this state is very sensitive to weak interactions, compared to those stabilizing a crystalline state, and to anisotropies. Moreover, under suitable conditions a 2D system in a striped phase decouples into (quasi) 1D chains. These observations are based on results of our studies of an extension of a microscopic quantum model of crystallization, proposed originally by Kennedy and Lieb.

cond-mat.str-el↗
arXiv2005

Exact results for spatial decay of correlations in low-dimensional insulators II

We study decay rates of one-body reduced density matrices in insulators, described by a tight-binding model, where not only an external potential but also hoppings are spatially modulated. We determine analytically the power in the power law and the correlation length in D=1 case and in several lattice directions in D=2 case. Unlike the uniform hopping case, in D=1 system and in some directions of D=2 system the correlation length is not determined uniquely by the gap. Moreover, a crossover from D=2-decay rates to D=1 ones is investigated.

cond-mat.other↗
arXiv2004

Formation of charge-stripe phases in a system of spinless fermions or hardcore bosons

We consider two strongly correlated two-component quantum systems, consisting of quantum mobile particles and classical immobile particles. The both systems are described by Falicov-Kimball-like Hamiltonians on a square lattice, extended by direct short-range interactions between the immobile particles. In the first system the mobile particles are spinless fermions while in the second one they are hardcore bosons. We construct rigorously ground-state phase diagrams of the both systems in the strong-coupling regime and at half-filling. Two main conclusions are drawn. Firstly, short-range interactions in quantum gases are sufficient for the appearance of charge stripe-ordered phases. By varying the intensity of a direct nearest-neighbor interaction between the immobile particles, the both systems can be driven from a phase-separated state (the segregated phase) to a crystalline state (the chessboard phase) and these transitions occur necessarily via charge-stripe phases: via a diagonal striped phase in the case of fermions and via vertical (horizontal) striped phases in the case of hardcore bosons. Secondly, the phase diagrams of the two systems (mobile fermions or mobile hardcore bosons) are definitely different. However, if the strongest effective interaction in the fermionic case gets frustrated gently, then the phase diagram becomes similar to that of the bosonic case.

cond-mat.str-el↗
arXiv2004

From phase separation to long-range order in a system of interacting electrons

We study a system composed of fermions (electrons), hopping on a square lattice, and of immobile particles (ions), that is described by the spinless Falicov-Kimball Hamiltonian augmented by a next-nearest-neighbor attractive interaction between the ions (a nearest-neighbor repulsive interaction between the ions can be included and does not alter the results). A part of the grand-canonical phase diagram of this system is constructed rigorously, when the coupling between the electrons and ions is much stronger than the hopping intensity of electrons. The obtained diagram implies that, at least for a few rational densities of particles, by increasing the hopping intensity the system can be driven from a state of phase separation to a state with a long-range order. This kind of transitions occurs also, when the hopping fermions are replaced by hopping hard-core bosons.

cond-mat.str-el↗
arXiv2004

Exact results for spatial decay of the one-body density matrix in low-dimensional insulators

We provide a tight-binding model of insulator, for which we derive an exact analytic form of the one-body density matrix and its large-distance asymptotics in dimensions $D=1,2$. The system is built out of a band of single-particle orbitals in a periodic potential. Breaking of the translational symmetry of the system results in two bands, separated by a direct gap whose width is proportional to the unique energy parameter of the model. The form of the decay is a power law times an exponential. We determine the power in the power law and the correlation length in the exponential, versus the lattice direction, the direct-gap width, and the lattice dimension. In particular, the obtained exact formulae imply that in the diagonal direction of the square lattice the inverse correlation length vanishes linearly with the vanishing gap, while in non-diagonal directions, the linear scaling is replaced by the square root one. Independently of direction, for sufficiently large gaps the inverse correlation length grows logarithmically with the gap width.

cond-mat.stat-mech↗
arXiv2003

Spatial decay of the one-body density matrix in insulators revised

In the framework of the band theory, we consider two tight-binding models of insulators. The first one, proposed recently by Taraskin et al, is a translationally invariant system, built out of two independent non-overlapping bands of single-particle orbitals that are coupled by a weak inter-band hybridization. This kind of insulator exhibits unphysical properties: we show, in particular, that the one-body density matrix does not depend on the width of the gap between the bands. Consequently, there is no delocalization effect with increasing metallicity. In the second model there are also two bands. However, they are not imposed by construction but are created from a band of single-particle orbitals due to the breaking of the translational symmetry by a periodic potential. These bands are separated by a gap for all nonzero values of the unique energy parameter of the model. We demonstrate that the one-body density matrix has the same structure as in the first model. As a result, the large distance asymptotic formulae derived by Taraskin et al in dimensions $D=1,2,3$, apply as well, but only for very large gap widths. In D=1 and in the diagonal direction of D=2 cases, we derive a stronger asymptotic formula, valid for all gap widths. The both kinds of asymptotic formulae are composed of a dimension-dependent power-law factor and a gap-dependent exponentially decaying factor. The latter asymptotics implies that the exponential decay rate vanishes linearly with the vanishing gap. In non-diagonal directions, we have found numerically that the linear scaling is replaced by the square root one. Independently of the direction, the exponential decay rate grows logarithmically with the gap width, for sufficiently large gaps.

cond-mat.stat-mech↗
arXiv2003

Ground-state properties of multicomponent Falicov-Kimball-like models I

We consider a classical lattice gas that consists of more than one "species" of particles (like a spin-3/2 Ising model or the atomic limit of the extended Hubbard model), whose ground-state phase diagram is macroscopically degenerate. This gas is coupled component-wise and in the Falicov-Kimball-like manner to a multicomponent free-fermion gas. We show rigorously that a component-wise coupling of the classical subsystem to the quantum one orders the classical subsystem so that the macroscopic degeneracy is removed.

cond-mat.stat-mech↗
arXiv1999

Devil's staircase for a nonconvex interaction

We study ground-state orderings of particles in classical lattice-gas models of adsorption on crystal surfaces. In the considered models, the energy of adsorbed particles is a sum of two components, each one representing the energy of a one-dimensional lattice gas with two-body interactions in one of the two orthogonal lattice directions. This feature reduces the two-dimensional problem to a one-dimensional one. The interaction energy in each direction is repulsive and strictly convex only from distance 2 on, while its value at distance 1 can be positive or negative, but close to zero. We show that if the decay rate of the interactions is fast enough, then particles form 2-particle lattice-connected aggregates which are distributed in the same most homogeneous way as particles whose interaction is strictly convex everywhere. Moreover, despite the lack of convexity, the density of particles versus the chemical potential appears to be a fractal curve known as the complete devil's staircase.

cond-mat.stat-mech↗
arXiv1999

Ground states of lattice gases with ``almost'' convex repulsive interactions

To our best knowledge there is only one example of a lattice system with long-range two-body interactions whose ground states have been determined exactly: the one-dimensional lattice gas with purely repulsive and strictly convex interactions. Its ground-state particle configurations do not depend on the rate of decay of the interactions and are known as the generalized Wigner lattices or the most homogenenous particle configurations. The question of stability of this beautiful and universal result against certain perturbations of the repulsive and convex interactions seems to be interesting by itself. Additional motivations for studying such perturbations come from surface physics (adsorbtion on crystal surfaces) and theories of correlated fermion systems (recent results on ground-state particle configurations of the one-dimensional spinless Falicov-Kimball model). As a first step we have studied a one-dimensional lattice gas whose two-body interactions are repulsive and strictly convex only from distance 2 on while its value at distance 1 is fixed near its value at infinity. We show that such a modification makes the ground-state particle configurations sensitive to the decay rate of the interactions: if it is fast enough, then particles form 2-particle lattice-connected aggregates that are distributed in the most homogeneous way. Consequently, despite breaking of the convexity property, the ground state exibits the feature known as the complete devil's staircase.

cond-mat.stat-mech↗