arXiv subjects

Gennady Y. Chitov

Publications and source records attributed to Gennady Y. Chitov.

At least 19 recordsLinked to original sources

arXiv2026

Topology of the Fermi surface and universality of the metal-metal and metal-insulator transitions: $d$-dimensional Hatsugai-Kohmoto model as an example

The earlier theory [1] of the quantum phase transitions related to the change of the Fermi Surface Topology (FST) is advanced. For such transitions the Fermi surface as a quantum critical manifold determined by the Lee-Yang zeros, the order parameter $\mathcal{P}$ as the $d$-volume of the Fermi sea, and the special FST universality class were introduced in [1]. The exactly solvable Hatsugai-Kohmoto (HK) $d$-dimensional ($d=1,2,3$) model of interacting fermions is analyzed. We explore the relation between the Lee-Yang zeros, the Luttinger and the plateau (Oshikawa) theorems. The validity of the Luttinger theorem in the HK model is confirmed. It is shown that the order parameter $\mathcal{P}$ and the FST universality class describe the transitions between metal and band/Mott insulators, as well as the Lifshitz and van Hove gapless-to-gapless transitions. The gapless phases are established to be the Landau Fermi liquids (metals). In addition to the conventional paradigm with a continuous order parameter, we apply the homology theory to analyze the FST transitions. They are critical points of the Morse function. To quantify FST we use the Euler characteristic, which is calculated for each phase of the HK model. We claim that the FST universality class is robust with respect to interactions and other model details, under the condition that the critical points are non-degenerate.

cond-mat.str-el↗

arXiv2026

Unwithered Majorana fermions in the bulk of a quantum chain

The proposal is to probe Majorana modes in the system when its parameters are tuned to bring it into a disentangled ground state, which occur on the parametric curves known as disorder lines (DL). In such state certain correlation functions do not depend on separation. The exact results are presented for the XY spin chain in transverse field, also called the Kitaev chain in the Majorana representation. The single Majorana modes are shown to be localized near the ends of the chain, as in the states off the DL, while the disentangled $n$-particle Majorana modes ($n \geq 2$) penetrate into the bulk without attenuation. The predicted bulk-edge effects can be detected in the specially engineered optical chains and lattices.

cond-mat.str-el↗

arXiv2025

Identifying internal patterns in (1+1)-dimensional directed percolation using neural networks

In this paper we present a neural network-based method for the automatic detection of phase transitions and classification of hidden percolation patterns in a (1+1)-dimensional replication process. The proposed network model is based on the combination of CNN, TCN and GRU networks, which are trained directly on raw configurations without any manual feature extraction. The network reproduces the phase diagram and assigns phase labels to configurations. It shows that deep architectures are capable of extracting hierarchical structures from the raw data of numerical experiments.

cs.LG↗

arXiv2025

Fermi surface as a quantum critical manifold: gaplessness, order parameter, and scaling in $d$-dimensions

We study several models of $d$-dimensional fermions ($d=1,2,3$) with an emphasis on the properties of their gapless (metallic) phase. It occurs at $T = 0$ as a continuous transition when zeros of the partition function reach the real range of parameters. Those zeros define the $(d-1)$-manifold of quantum criticality (Fermi surface). Its appearance or restructuring correspond to the Lifshitz transition. Such $(d-1)$-membrane breaks the symmetry of the momentum space, leading to gapless excitations, a hallmark of metallic phase. To probe quantitatively the gapless phase we introduce the geometric order parameter as $d$-volume of the Fermi sea. From analysis of the chain, ladder, and free fermions with different spectra, this proposal is shown to be consistent with scaling near the Lifshitz points of other quantities: correlation length, oscillation wavelength, susceptibilities, and entanglement. All the (hyper)scaling relations are satisfied. Two interacting cases of the Tomonaga-Luttinger ($d=1$) and the Fermi ($d=2,3$) liquids are analysed, yielding the same universality classes as free fermions.

cond-mat.str-el↗

arXiv2024

Observational Constraints on Dynamical Dark Energy Models

$ϕ$CDM models provide an alternative to the standard $Λ$CDM paradigm, while being physically better motivated. These models lead to a time-dependent speed of sound for dark energy that is difficult to replicate by $w$CDM parametrizations. We review the most up-to-date status of observational evidence for the $ϕ$CDM models in this paper. We start with an overview of the motivation behind these classes of models, the basic mathematical formalism, and the different classes of models. We then present a compilation of recent results of applying different observational probes to constraining $ϕ$CDM model parameters. Over the last twenty years, the precision of observational data has increased immensely, leading to ever tighter constraints. A combination of the recent measurements favors the spatially flat $Λ$CDM model, but a large class of $ϕ$CDM models is still not ruled out.

astro-ph.CO↗

arXiv2022

Disentanglement, disorder lines, and Majorana edge states in a solvable quantum chain

We study the exactly solvable 1D model: the dimerized $XY$ chain with uniform and staggered transverse fields, equivalent upon fermionization to the noninteracting dimerized Kitaev-Majorana chain with modulation. The model has three known gapped phases with local and nonlocal (string) orders, along with the gapless incommensurate (IC) phase in the $U(1)$ limit. The criticality is controlled by the properties of zeros of model's partition function, analytically continued onto the complex wave numbers. In the ground state they become complex zeros of the spectrum of the Hamiltonian. The analysis of those roots yields the phase diagram which contains continuous quantum phase transitions and weaker singularities known as disorder lines (DLs) or modulation transitions. The latter, reported for the first time in this model, are shown to occur in two types: DLs of the first kind with continuous appearance of the IC oscillations, and DLs of the second kind corresponding to a jump of the wave number of oscillations. The salient property of zeros of the spectrum is that the ground state is shown to be separable (factorized) and the model is disentangled on a subset of the DLs. From analysis of those zeros we also find the Majorana edge states and their wave functions.

cond-mat.str-el↗

arXiv2022

Brane order and quantum magnetism in modulated anisotropic ladders

Two-leg spin-$\frac12$ ladders with anisotropy and two different dimerization patterns are analyzed at zero temperature. This model is equivalent to a modulated interacting (Kitaev) ladder. The Hartree-Fock mean-field approximation reduces the model to a sum of two quadratic effective Majorana Hamiltonians, which are dual to a sum of two (even/odd) XY quantum chains in the alternating transverse fields. The mapping between the effective Hamiltonian of the ladder and the pair of the dual XY chains considerably simplifies calculations the order parameters and analysis of the hidden symmetry breaking. The ground-state phase diagram of the staggered ladder contains nine phases, four of them are conventional antiferromagnets, while the other five possess non-local brane orders. Using the dualities and the newly found exact results for the local and string order parameters of the transverse XY chains, we were able to find analytically all the magnetizations and the brane order parameters for the staggered case, as functions of the renormalized couplings of the effective Hamiltonian. The columnar ladder has three ground-state phases and does not possess magnetic long-ranged order. The brane order parameters for these three phases are calculated numerically from the Toeplitz determinants. We expect this study to motivate the search for the real spin-Peierls anisotropic ladder compounds which can undergo the predicted quantum phase transitions with gap closures and distinct brane orders.

cond-mat.str-el↗

arXiv2021

Disorder lines, modulation, and partition function zeros in free fermion models

The modulation is analyzed from the analytical properties of zeros of free fermionic partition function on the complex plane of wave numbers. It is shown how these properties are related to the oscillations of correlation functions. This approach can be used for analysis of phase transitions with local or nonlocal order parameters, as well as for the disorder lines. We find an infinite cascade of disorder lines at finite temperature in the quantum $XY$ chain (equivalent to free fermions). The well-known ground state factorization on the disorder line, and consequently, disentanglement, is shown to follow directly from analytical properties of this model on the complex plane. From the quantum-classical correspondence the results for the chain are used to detect the disorder lines in several frustrated 2D Ising models. The present formalism can be applied to other fermionic models in two and three spatial dimensions. In particular, we find the temperature-dependent Fermi wave vector of oscillations in the degenerate gas of 3D fermions, which naturally leads in the limit $T \to 0$ to the definition of the Fermi energy as the surface of quantum criticality. The modulation is a very common phenomenon, and it occurs in a large variety of models. The important point is that all these modulation transitions can be related to the complex zeros of partition functions, as done in the present study.

cond-mat.str-el↗

arXiv2021

Mass varying neutrinos with different quintessence potentials

The mass-varying neutrino scenario is analyzed for three trial quintessence potentials (Ferreira-Joyce, inverse exponential, and thawing oscillating). The neutrino mass is generated via Yukawa coupling to the scalar field which represents dark energy. The inverse exponential and oscillating potentials are shown to successfully generate the neutrino masses in the range $m \sim 10^{-2}-10^{-3}~$eV and to yield the current dark energy density in the regime of the late-time acceleration of the Universe. Depending on the choice of potentials, the acceleration could occur in two different regimes: (1) the regime of instability, and (2) the stable regime. The first regime of instability is after the Universe underwent a first-order transition and is rolling toward the new stable vacuum. The imaginary sound velocity $c^2_s < 0$ in this regime implies growing fluctuations of the neutrino density (clustering). In the second regime, the Universe smoothly changes its stable states via a continuous transition. Since $c^2_s > 0$, the neutrino density is stable. For all cases the predicted late-time acceleration of the Universe is asymptotically very close to that of the $Λ$CDM model. Further extensions of the theory to modify the neutrino sector of the Standard Model and to incorporate inflation are also discussed. It is also shown that in the stable regimes where the neutrino mass is given by the minimum of the thermodynamic potential, the tree-level dynamics of the scalar field is robust with respect to one-loop bosonic and fermionic corrections to the potential.

hep-ph↗

arXiv2020

Phase diagram and topological order in the modulated $XYZ$ chain with magnetic fields

The $XYZ$ antiferromagnetic spin-$1/2$ chain with alternation of the exchange and anisotropy couplings in the presence of uniform and staggered axial magnetic fields is studied. The analysis is done using the effective quadratic fermionic Hamiltonian resulting from the Hartee-Fock approximation. Combining the exact and the mean-field methods, the local and string order parameters on the ground-state phase diagram of the model are identified and calculated. We found a topological phase with oscillating string order with a period of four lattice spacings, not reported before for this model. A detailed analysis of patterns of the string order is given. The special $XXZ$ limit of the model with additional $U(1)$ symmetry brings about, in agreement with the Lieb-Schultz-Mattis theorem and its extensions, plateaux of magnetization and some additional conserving quantities. We have shown that in the $XYZ$ chain, where the plateaux are smeared, the robust oscillating string order parameter is continuously connected to its $XXZ$ limit. Also, the non-trivial winding number and zero-energy localized Majorana edge states, as additional attributes of topological order, are robust in that phase, even off the line of $U(1)$ symmetry.

cond-mat.str-el↗

arXiv2019

String and conventional order parameters in the solvable modulated quantum chain

The phase diagram and the order parameters of the exactly solvable quantum 1D model are analysed. The model in its spin representation is the dimerized XY spin chain in the presence of uniform and staggered transverse fields. In the fermionic representation this model is the dimerized non-interacting Kitaev chain with a modulated chemical potential. The model has a rich phase diagram which contains phases with local and non-local (string) orders. We have calculated within the same systematic framework the local order parameters (spontaneous magnetization) and the non-local string order parameters, along with the topological winding numbers for all domains of the phase diagram. The topologically nontrivial phase is shown to have a peculiar oscillating string order with the wavenumber $q=π/2$, awaiting for its experimental confirmation.

cond-mat.stat-mech↗

arXiv2018

Local and nonlocal order parameters in the Kitaev chain

We have calculated order parameters for the phases of the Kitaev chain with interaction and dimerization at a special symmetric point applying the Jordan-Wigner and other duality transformations. We use string order parameters (SOPs) defined via the correlation functions of the Majorana string operators. The SOPs are mapped onto the local order parameters of some dual Hamiltonians and easily calculated. We have shown that the phase diagram of the interacting dimerized chain comprises the phases with the conventional local order as well as the phases with nonlocal SOPs. From the results for the critical indices we infer the 2D Ising universality class of criticality at the particular symmetry point where the model is exactly solvable.

cond-mat.str-el↗

arXiv2017

Infinite cascades of phase transitions in the classical Ising chain

We report the new exact results on one of the best studied models in statistical physics: the classical antiferromagnetic Ising chain in a magnetic field. We show that the model possesses an infinite cascade of thermal phase transitions (also known as "disorder lines" or geometric phase transitions). The phase transition is signalled by a change of asymptotic behavior of the nonlocal string-string correlation functions when their monotonous decay becomes modulated by incommensurate oscillations. The transitions occur for rarefied ($m$-periodic) strings with arbitrary odd $m$. We propose a duality transformation which maps the Ising chain onto the $m$-leg Ising tube with nearest-neighbor couplings along the legs and the plaquette four-spin interactions of adjacent legs. Then the $m$-string correlation functions of the Ising chain are mapped onto the two-point spin-spin correlation functions along the legs of the $m$-leg tube. We trace the origin of these cascades of phase transitions to the lines of the Lee-Yang zeros of the Ising chain in $m$-periodic complex magnetic field, allowing us to relate these zeros to the observable (and potentially measurable) quantities.

cond-mat.stat-mech↗

arXiv2017

Constructing Landau framework for topological order: Quantum chains and ladders

We studied quantum phase transitions in the antiferromagnetic dimerized spin-1/2 XY chain andvtwo-leg ladders. From analysis of several spin models we present our main result: the framework to deal with topological orders and hidden symmetries within the Landau paradigm. After mapping of the spin Hamiltonians onto the tight-binding models with Dirac or Majorana fermions and, when necessary, the mean-field approximation, the analysis can be done analytically. By utilizing duality transformations the calculation of nonlocal string order parameters is mapped onto the local order problem in some dual representation and done without further approximations. Calculated phase diagrams, phase boundaries, order parameters and their symmetries for each of the phases provide a comprehensive quantitative Landau description of the quantum critical properties of the models considered. Complementarily, the phases with hidden orders can also be distinguished by the Pontryagin (winding) numbers which we have calculated as well. This unified framework can be straightforwardly applied for various spin chains and ladders, topological insulators and superconductors. Applications to other systems are under way.

cond-mat.str-el↗

arXiv2015

Exploring Percolative Landscapes: Infinite Cascades of Geometric Phase Transitions

The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2d directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process (CP) we show from the Monte-Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometric transitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions is a generic feature of percolation as well as many others transitions with nonlocal order parameters.

cond-mat.stat-mech↗

arXiv2011

Quintessence, Neutrino Masses and Unification of the Dark Sector

The origin of the neutrino mass, dark matter (DM), and dark energy (DE) are among the most challenging problems of fundamental physics. We address these questions from analyses of the models where the neutrino mass is generated via Yukawa coupling to the quintessence field which represents the DE. It has been shown in a recent work on the toy model with a single Dirac fermion coupled to the quintessence that by choosing parameters of the DE potential to match the present DE density, the model allows to lock the neutrino mass at m ~0.01 eV and yields consistent estimates for other parameters of the Universe. To include the DM component into this framework we propose here to add the right-handed Majorana term(s) into Lagrangian with the quintessence-generated mass. As a results, the DE field is responsible for generation of the masses of the light active Majorana neutrinos as well as of the heavy sterile neutrinos. The latter are natural DM candidates.

hep-ph↗

arXiv2011

The gap vs critical temperature ratio in Peierls-type phase transitions

We analyze a 2D spin-pseudospin model, where the pseudospins represents the charge degrees of freedom. The model is known to undergo a phase transition with the simultaneous appearance of the long-range charge order and the spin gap. We show how the gap vs critical temperature ratio (also called the BCS ratio) gets renormalized from the classical non-interacting value. This value is also universal in the sense that is does not depend on the microscopic parameters of the model, and must be the same for various types of the Peierls-like transitions where the spin gap is accompanied by the structural, orbital or charge order.

cond-mat.str-el↗

arXiv2007

Quantum Criticality in Dimerized Spin Ladders

We analyze a possibility of quantum criticality (gaplessness) in dimerized antiferromagnetic two- and three-leg spin-1/2 ladders. Contrary to earlier studies of these models, we examine different dimerization patterns in the ladder. We find that ladders with the columnar dimerization order have lower zero-temperature energies and they are always gapped. For the staggered dimerization order, we find the quantum critical lines, in agreement with earlier analyses. The bond mean-field theory we apply, demonstrates its quantitative accuracy and agrees with available numerical results. We conclude that unless some mechanism for locking dimerization into the energetically less favorable staggered configuration is provided, the dimerized ladders do not order into the phase where the quantum criticality occurs.

cond-mat.str-el↗