arXiv subjects

Taras Krokhmalskii

Publications and source records attributed to Taras Krokhmalskii.

At least 37 records · Page 2Linked to original sources

arXiv2015

Quantum phase transitions and ground-state correlations in BCS-like models

We study ground-state correlation functions in one- and two-dimensional lattice models of interacting spinful fermions - BCS-like models, which exhibit continuous quantum phase transitions. The considered models originate from a two-dimensional model of d-wave superconductivity proposed by Sachdev. Due to the exact diagonalizability of the considered models in any dimensionality, exact phase diagrams, with several kinds of quantum-critical points, are constructed and closed-form analytic expressions for two-point correlation functions are obtained. In one- and two-dimensional cases we provide analytic expressions for the asymptotic behavior of those correlation functions at large distances and in neighborhoods of quantum-critical points. The novelty of our results is that in two-dimensions explicit expressions for direction-dependent correlation lengths in terms of model parameters and the values of direction-dependent universal critical indices $ν$, that characterize the divergence of correlation lengths on approaching critical points, are determined. Moreover, specific scaling properties of correlation functions with respect to parameters of underlying Hamiltonians are revealed. Besides enriching the knowledge of properties of lattice fermion systems exhibiting continuous quantum phase transitions, especially in two dimensions, our results open new possibilities of testing unconventional methods of studying quantum phase transitions, as the promising fidelity approach or the entanglement approach, beyond one-dimension and beyond the realm of paradigmatic XY and Ising chains in transverse magnetic fields.

cond-mat.stat-mech↗

arXiv2014

Frustrated diamond-chain quantum $XXZ$ Heisenberg antiferromagnet in a magnetic field

We consider the antiferromagnetic spin-1/2 $XXZ$ Heisenberg model on a frustrated diamond-chain lattice in a $z$- or $x$-aligned external magnetic field. We use the strong-coupling approach to elaborate an effective description in the low-temperature strong-field regime. The obtained effective models are spin-1/2 $XY$ chains which are exactly solvable through the Jordan-Wigner fermionization. We perform exact-diagonalization studies of the magnetization curves to test the quality of the effective description. The results may have relevance for the description of the azurite spin-chain compound.

cond-mat.str-el↗

arXiv2013

The square-kagome quantum Heisenberg antiferromagnet at high magnetic fields: The localized-magnon paradigm and beyond

We consider the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional square-kagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate low-energy effective Hamiltonians which emerge at high magnetic fields. The effective model to describe the low-energy degrees of freedom of the initial frustrated quantum spin model is the (unfrustrated) square-lattice spin-1/2 $XXZ$ model in a $z$-aligned magnetic field. For the effective model we perform quantum Monte Carlo simulations to discuss the low-temperature properties of the square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We pay special attention to a magnetic-field driven Berezinskii-Kosterlitz-Thouless phase transition which occurs at low temperatures.

cond-mat.str-el↗

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↗

arXiv2013

Frustrated quantum Heisenberg antiferromagnets at high magnetic fields: Beyond the flat-band scenario

We consider the spin-1/2 antiferromagnetic Heisenberg model on three frustrated lattices (the diamond chain, the dimer-plaquette chain and the two-dimensional square-kagome lattice) with almost dispersionless lowest magnon band. Eliminating high-energy degrees of freedom at high magnetic fields, we construct low-energy effective Hamiltonians which are much simpler than the initial ones. These effective Hamiltonians allow a more extended analytical and numerical analysis. In addition to the standard strong-coupling perturbation theory we also use a localized-magnon based approach leading to a substantial improvement of the strong-coupling approximation. We perform extensive exact diagonalization calculations to check the quality of different effective Hamiltonians by comparison with the initial models. Based on the effective-model description we examine the low-temperature properties of the considered frustrated quantum Heisenberg antiferromagnets in the high-field regime. We also apply our approach to explore thermodynamic properties for a generalized diamond spin chain model suitable to describe azurite at high magnetic fields. Interesting features of these highly frustrated spin models consist in a steep increase of the entropy at very small temperatures and a characteristic extra low-temperature peak in the specific heat. The most prominent effect is the existence of a magnetic-field driven Berezinskii-Kosterlitz-Thouless phase transition occurring in the two-dimensional model.

cond-mat.str-el↗

arXiv2012

Magnetocaloric effect in spin-1/2 $XX$ chains with three-spin interactions

We consider the exactly solvable spin-1/2 $XX$ chain with the three-spin interactions of the $XZX+YZY$ and $XZY-YZX$ types in an external (transverse) magnetic field. We calculate the entropy and examine the magnetocaloric effect for the quantum spin system. We discuss a relation between the cooling/heating efficiency and the ground-state phase diagram of the quantum spin model. We also compare ability to cool/heat in the vicinity of the quantum critical and triple points. Moreover, we examine the magnetocaloric effect for the spin-1/2 $XX$ chain with three-spin interactions in a random (Lorentzian) transverse magnetic field.

cond-mat.str-el↗

arXiv2011

Quantum Heisenberg antiferromagnet on low-dimensional frustrated lattices

Using a lattice-gas description of the low-energy degrees of freedom of the quantum Heisenberg antiferromagnet on the frustrated two-leg ladder and bilayer lattices we examine the magnetization process at low temperatures for these spin models. In both cases the emergent discrete degrees of freedom implicate a close relation of the frustrated quantum Heisenberg antiferromagnet to the classical lattice gas with finite nearest-neighbor repulsion or, equivalently, to the Ising antiferromagnet in a uniform magnetic field. Using this relation we obtain analytical results for thermodynamically large systems in the one-dimensional case. In the two-dimensional case we perform classical Monte Carlo simulations for systems of up to $100 \times 100$ sites.

cond-mat.str-el↗

arXiv2010

Emergent Ising degrees of freedom in frustrated two-leg ladder and bilayer $s=1/2$ Heisenberg antiferromagnets

Based on exact diagonalization data for finite quantum Heisenberg antiferromagnets on two frustrated lattices (two-leg ladder and bilayer) and analytical arguments we map low-energy degrees of freedom of the spin models in a magnetic field on classical lattice-gas models. Further we use transfer-matrix calculations and classical Monte Carlo simulations to give a quantitative description of low-temperature thermodynamics of the quantum spin models. The classical lattice-gas model yields an excellent description of the quantum spin models up to quite large temperatures. The main peculiarity of the considered frustrated bilayer is a phase transition which occurs at low temperatures for a wide range of magnetic fields below the saturation magnetic field and belongs to the two-dimensional Ising model universality class.

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↗

arXiv2008

Dynamic properties of the spin-1/2 XY chain with three-site interactions

We consider a spin-1/2 XY chain in a transverse (z) field with multi-site interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan-Wigner transformation leads to a simple bilinear Fermi form for the resulting Hamiltonian and hence the spin model admits a rigorous analysis. We point out the close relationships between several variants of the model which were discussed separately in previous studies. The ground-state phases (ferromagnet and two kinds of spin liquid) of the model are reflected in the dynamic structure factors of the spin chains, which are the main focus in this study. First we consider the zz dynamic structure factor reporting for this quantity a closed-form expression and analyzing the properties of the two-fermion (particle-hole) excitation continuum which governs the dynamics of transverse spin component fluctuations and of some other local operator fluctuations. Then we examine the xx dynamic structure factor which is governed by many-fermion excitations, reporting both analytical and numerical results. We discuss some easily recognized features of the dynamic structure factors which are signatures for the presence of the three-site interactions.

cond-mat.str-el↗

arXiv2008

Dynamic properties of quantum spin chains: Simple route to complex behavior

We examine dynamic structure factors of spin-1/2 chains with nearest-neighbor interactions of XX and Dzyaloshinskii-Moriya type, and with periodic and random changes in the sign of these interactions. This special kind of inhomogeneity can be eliminated from the Hamiltonian by suitable transformation of the spin variables. As a result, the dynamic structure factors of periodic or random chains can be computed from those of the uniform chains. Using the exact analytical and precise numerical results available for the uniform systems we illustrate the effects of regular alternation or random disorder on dynamic structure factors of quantum spin chains.

cond-mat.str-el↗

arXiv2007

Dynamic probes of quantum spin chains with the Dzyaloshinskii-Moriya interaction

We consider the spin-1/2 anisotropic XY chain in a transverse (z) field with the Dzyaloshinskii-Moriya interaction directed along z-axis in spin space to examine the effect of the Dzyaloshinskii-Moriya interaction on the zz, xx and yy dynamic structure factors. Using the Jordan-Wigner fermionization approach we analytically calculate the dynamic transverse spin structure factor. It is governed by a two-fermion excitation continuum. We analyze the effect of the Dzyaloshinskii-Moriya interaction on the two-fermion excitation continuum. Other dynamic structure factors which are governed by many-fermion excitations are calculated numerically. We discuss how the Dzyaloshinskii-Moriya interaction manifests itself in the dynamic properties of the quantum spin chain at various fields and temperatures.

cond-mat.str-el↗

arXiv2006

Finite-temperature order-disorder phase transition in a frustrated bilayer quantum Heisenberg antiferromagnet in strong magnetic fields

We investigate the thermodynamic properties of the frustrated bilayer quantum Heisenberg antiferromagnet at low temperatures in the vicinity of the saturation magnetic field. The low-energy degrees of freedom of the spin model are mapped onto a hard-square gas on a square lattice. We use exact diagonalization data for finite spin systems to check the validity of such a description. Using a classical Monte Carlo method we give a quantitative description of the thermodynamics of the spin model at low temperatures around the saturation field. The main peculiarity of the considered two-dimensional Heisenberg antiferromagnet is related to a phase transition of the hard-square model on the square lattice, which belongs to the two-dimensional Ising model universality class. It manifests itself in a logarithmic (low-)temperature singularity of the specific heat of the spin system observed for magnetic fields just below the saturation field.

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↗

arXiv2005

Dimer and trimer fluctuations in the s=1/2 transverse XX chain

Exact results for the dynamic dimer and trimer structure factors of the one-dimensional s=1/2 XX model in a transverse magnetic field ($\parallel z$) are presented and discussed in relation to known exact results for the dynamic spin structure factors. In the framework of the Jordan-Wigner representation, the accessible spectrum of the dimer fluctuation operator is limited to two-fermion excitations whereas that of the trimer fluctuation operator involves two-fermion and four-fermion excitations. The spectral boundaries, soft modes, and singularity structure of the four-fermion excitation continuum as probed by the dynamic trimer structure factor are examined and compared with corresponding properties of the two-fermion excitation continuum, as probed by the dynamic dimer and transverse spin structure factors.

cond-mat.stat-mech↗

arXiv2005

Quantum Phase Transitions in Spin-1/2 Ising Chain in Regularly Alternating Transverse Field: Spin Correlation Functions

We consider the spin-1/2 Ising chain in a regularly alternating transverse field to examine the effects of regular alternation on the quantum phase transition inherent in the quantum Ising chain. The number of quantum phase transition points strongly depends on the specific set of the Hamiltonian parameters but never exceeds 2p where p is the period of alternation. Calculating the spin correlation functions numerically (for long chains of up to 5400 sites) and determining the critical exponents we have demonstrated that two types of critical behavior are possible. In most cases the square-lattice Ising model universality class occurs, however, a weaker singularity may also take place.

cond-mat.stat-mech↗

arXiv2005

Jordan-Wigner Approach to Dynamic Correlations in 2D Spin-1/2 Models

We discuss the dynamic properties of the square-lattice spin-1/2 XY model obtained using the two-dimensional Jordan-Wigner fermionization approach. We argue the relevancy of the fermionic picture for interpreting the neutron scattering measurements in the two-dimensional frustrated quantum magnet Cs_2CuCl_4.

cond-mat.str-el↗

arXiv2005

Quantum Phase Transitions in s=1/2 Ising Chain in a Regularly Alternating Transverse Field

We consider the ground-state properties of the s=1/2 Ising chain in a transverse field which varies regularly along the chain having a period of alternation 2. Such a model, similarly to its uniform counterpart, exhibits quantum phase transitions. However, the number and the position of the quantum phase transition points depend on the strength of transverse field modulation. The behaviour in the vicinity of the critical field in most cases remains the same as for the uniform chain (i.e. belongs to the square-lattice Ising model universality class). However, a new critical behaviour may also arise. We report the results for critical exponents obtained partially analytically and partially numerically for very long chains consisting of a few thousand sites.

cond-mat.stat-mech↗