arXiv subjects

Vladimir Gritsev

Publications and source records attributed to Vladimir Gritsev.

At least 37 records · Page 2Linked to original sources

arXiv2021

Topological field theory approach to intermediate statistics

Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral form factor (SFF). Here, we calculate the SFF of unitary matrix ensembles of infinite order with the weight function satisfying the assumptions of Szegö's limit theorem. We then consider a parameter-dependent critical ensemble which has intermediate statistics characteristic of ergodic-to-nonergodic transitions such as the Anderson localization transition. This same ensemble is the matrix model of $U(N)$ Chern-Simons theory on $S^3$, and the SFF of this ensemble is proportional to the HOMFLY invariant of $(2n,2)$-torus links with one component in the fundamental and one in the antifundamental representation. This is one of a large class of ensembles arising from topological field and string theories which exhibit intermediate statistics. Indeed, the absence of a local order parameter suggests that it is natural to characterize ergodic-to-nonergodic transitions using topological tools, such as we have done here.

cond-mat.str-el↗

arXiv2021

Hidden Symmetries, the Bianchi Classification and Geodesics of the Quantum Geometric Ground-State Manifolds

We study the Killing vectors of the quantum ground-state manifold of a parameter-dependent Hamiltonian. We find that the manifold may have symmetries that are not visible at the level of the Hamiltonian and that different quantum phases of matter exhibit different symmetries. We propose a Bianchi-based classification of the various ground-state manifolds using the Lie algebra of the Killing vector fields. Moreover, we explain how to exploit these symmetries to find geodesics and explore their behaviour when crossing critical lines. We briefly discuss the relation between geodesics, energy fluctuations and adiabatic preparation protocols. Our primary example is the anisotropic transverse-field Ising model. We also analyze the Ising limit and find analytic solutions to the geodesic equations for both cases.

cond-mat.stat-mech↗

arXiv2020

Quasi-conserved quantities in the perturbed XXX spin chain

We consider the isotropic spin-1/2 Heisenberg spin chain weakly perturbed by a local translationally- and SU(2)-invariant perturbation. Starting from the local integrals of motion of the unperturbed model, we modify them in order to obtain quasi-conserved integrals of motion (charges) for the perturbed model. Such quasi-conserved quantities are believed to be responsible for the existence of the prethermalization phase at intermediate timescales. We find that for a sufficiently local perturbation only the first few integrals of motion can be promoted to the quasi-conserved charges, whereas higher-order integrals of motion do not survive.

cond-mat.stat-mech↗

arXiv2020

Entanglement Dynamics of Random GUE Hamiltonians

In this work, we consider a model of a subsystem interacting with a reservoir and study dynamics of entanglement assuming that the overall time-evolution is governed by non-integrable Hamiltonians. We also compare to an ensemble of Integrable Hamiltonians. To do this, we make use of unitary invariant ensembles of random matrices with either Wigner-Dyson or Poissonian distributions of energy. Using the theory of Weingarten functions, we derive universal average time evolution of the reduced density matrix and the purity and compare these results with several physical Hamiltonians: randomized versions of the transverse field Ising and XXZ models, Spin Glass and, Central Spin and SYK model. The theory excels at describing the latter two. Along the way, we find general expressions for exponential $n$-point correlation functions in the gas of GUE eigenvalues.

quant-ph↗

arXiv2018

Random Matrix Ensemble for the Level Statistics of Many-Body Localization

We numerically study the level statistics of the Gaussian $β$ ensemble. These statistics generalize Wigner-Dyson level statistics from the discrete set of Dyson indices $β= 1,2,4$ to the continuous range $0 < β< \infty$. The Gaussian $β$ ensemble covers Poissonian level statistics for $β\to 0$, and provides a smooth interpolation between Poissonian and Wigner-Dyson level statistics. We establish the physical relevance of the level statistics of the Gaussian $β$ ensemble by showing near-perfect agreement with the level statistics of a paradigmatic model in studies on many-body localization over the entire crossover range from the thermal to the many-body localized phase. In addition, we show similar agreement for a related Hamiltonian with broken time-reversal symmetry.

cond-mat.dis-nn↗

arXiv2018

Something interacting and solvable in 1d

We present a two-parameter family of exactly solvable quantum many-body systems in one spatial dimension containing the Lieb-Liniger model of interacting bosons as a particular case. The principal building block of this construction is the previously-introduced (arXiv:1712.09375) family of two-particle scattering matrices. We discuss an $SL(2)$ transformation connecting the models within this family and make a correspondence with generalized point interactions. The Bethe equations for the ground state are discussed with a special emphasis on "non-interacting modes" connected by the modular subgroup of $SL(2)$. The bound state solutions are discussed and are conjectured to follow some correlated version of the string hypothesis. The excitation spectrum of the new models in this family is derived in analogy to the Lieb-Liniger model and we show that for certain choices of parameters a spectrum inversion occurs such that the Umklapp solutions become the new ground state.

cond-mat.other↗

arXiv2018

Integrable spin chains with random interactions

We study a Yang-Baxter integrable quantum spin-1/2 chain with random interactions. The Hamiltonian is local and involves two and three-spin interactions with random parameters. We show that the energy eigenstates of the model are never localized and in fact exhibit perfect energy and spin transport at both zero and infinite temperatures. By considering the vicinity of a free fermion point in the model we demonstrate that this behavior persists under deformations that break integrability but preserve the free fermion nature of the Hamiltonian. In this case the ballistic behavior can be understood as arising from the correlated nature of the disorder in the model. We conjecture that the model belongs to a broad class of models avoiding localization in 1D.

cond-mat.dis-nn↗

arXiv2018

Many-body localization in the Fock space of natural orbitals

We study the eigenstates of a paradigmatic model of many-body localization in the Fock basis constructed out of the natural orbitals. By numerically studying the participation ratio, we identify a sharp crossover between different phases at a disorder strength close to the disorder strength at which subdiffusive behaviour sets in, significantly below the many-body localization transition. We repeat the analysis in the conventionally used computational basis, and show that many-body localized eigenstates are much stronger localized in the Fock basis constructed out of the natural orbitals than in the computational basis.

cond-mat.dis-nn↗

arXiv2018

Symmetry-protected coherent relaxation of open quantum systems

We compute the effect of Markovian bulk dephasing noise on the staggered magnetization of the spin-1/2 XXZ Heisenberg chain, as the system evolves after a Néel quench. For sufficiently weak system-bath coupling, the unitary dynamics are found to be preserved up to a single exponential damping factor. This is a consequence of the interplay between $\mathbb{PT}$ symmetry and weak symmetries, which strengthens previous predictions for $\mathbb{PT}$-symmetric Liouvillian dynamics. Requirements are a non-degenerate $\mathbb{PT}$-symmetric generator of time evolution $\hat{\mathcal{L}}$, a weak parity symmetry and an observable that is anti-symmetric under this parity transformation. The spectrum of $\hat{\mathcal{L}}$ then splits up into symmetry sectors, yielding the same decay rate for all modes that contribute to the observable's time evolution. This phenomenon may be realized in trapped ion experiments and has possible implications for the control of decoherence in out-of-equilibrium many-body systems.

quant-ph↗

arXiv2018

Non-adiabatic effects in periodically driven-dissipative open quantum systems

We present a general method to calculate the quasi-stationary state of a driven-dissipative system coupled to a transmission line (and more generally, to a reservoir) under periodic modulation of its parameters. Using Floquet's theorem, we formulate the differential equation for the system's density operator which has to be solved for a single period of modulation. On this basis we also provide systematic expansions in both the adiabatic and high-frequency regime. Applying our method to three different systems -- two- and three-level models as well as the driven nonlinear cavity -- we propose periodic modulation protocols of parameters leading to a temporary suppression of effective dissipation rates, and study the arising non-adiabatic features in the response of these systems.

quant-ph↗

arXiv2018

Integrability and duality in spin chains

We construct a new, two-parametric family of integrable models and reveal their underlying duality symmetry. A modular subgroup of this duality is shown to connect non-interacting modes of different systems. We apply the new solution and duality to a Richardson-Gaudin model and generate a novel integrable system termed the $s$-$d$ wave Richardson-Gaudin-Kitaev interacting chain, interpolating $s$- and $d$- wave superconductivity. The phase diagram of this model has a topological phase transition that can be connected to the duality, where the occupancy of the non-interacting mode serves as a topological order parameter.

cond-mat.str-el↗

arXiv2017

Integrable Floquet dynamics

We discuss several classes of integrable Floquet systems, i.e. systems which do not exhibit chaotic behavior even under a time dependent perturbation. The first class is associated with finite-dimensional Lie groups and infinite-dimensional generalization thereof. The second class is related to the row transfer matrices of the 2D statistical mechanics models. The third class of models, called here "boost models", is constructed as a periodic interchange of two Hamiltonians - one is the integrable lattice model Hamiltonian, while the second is the boost operator. The latter for known cases coincides with the entanglement Hamiltonian and is closely related to the corner transfer matrix of the corresponding 2D statistical models. We present several explicit examples. As an interesting application of the boost models we discuss a possibility of generating periodically oscillating states with the period different from that of the driving field. In particular, one can realize an oscillating state by performing a static quench to a boost operator. We term this state a "Quantum Boost Clock". All analyzed setups can be readily realized experimentally, for example in cod atoms.

cond-mat.stat-mech↗

arXiv2017

Control over few photon pulses by a time-periodic modulation of the photon-emitter coupling

We develop a Floquet scattering formalism for the description of quasistationary states of microwave photons in a one-dimensional waveguide interacting with a nonlinear cavity by means of a periodically modulated coupling. This model is inspired by the recent progress in engineering of tunable coupling schemes with superconducting qubits. We argue that our model can realize the quantum analogue of an optical chopper. We find strong periodic modulations of the transmission and reflection envelopes in the scattered few-photon pulses, including photon compression and blockade, as well as dramatic changes in statistics. Our theoretical analysis allows us to explain these non-trivial phenomena as arising from non-adiabatic memory effects.

quant-ph↗

arXiv2017

Non-ergodicity in the Anisotropic Dicke model

We study the ergodic -- non-ergodic transition in a generalized Dicke model with independent co- and counter rotating light-matter coupling terms. By studying level statistics, the average ratio of consecutive level spacings, and the quantum butterfly effect (out-of-time correlation) as a dynamical probe, we show that the ergodic -- non-ergodic transition in the Dicke model is a consequence of the proximity to the integrable limit of the model when one of the couplings is set to zero. This can be interpreted as a hint for the existence of a quantum analogue of the classical Kolmogorov-Arnold-Moser theorem. Besides, we show that there is no intrinsic relation between the ergodic -- non-ergodic transition and the precursors of the normal -- superradiant quantum phase transition.

quant-ph↗

arXiv2016

Photonic Kondo model

Here we introduce and study a photonic analogue of the Kondo model. The model is defined as a far detuned regime of photonic scattering off a three-level emitter in a $Λ$-type configuration coupled to a one-dimensional transmission line with linear dispersion. We characterize this system by studying the dynamics of a local system (emitter) driven by a coherent field pulse as well as the first- and second-order correlation functions of the scattered light. Various polarization-dependent correlation effects including entanglement between the emitter and transmitted photons are quantified by the purity of the emitter's state. We also show that statistical properties of the scattered light are very sensitive to the polarization of the incoming coherent pulse.

quant-ph↗

arXiv2016

Quantum choppers

An optical chopper periodically interrupts a classical light beam. We propose a realizable quantum version of the optical chopper, where the time-periodic driving of the light-matter coupling is achieved through a nonlinear three wave mixing element. We theoretically investigate how our scheme can be used for the controllable shaping of few photon light. Using Floquet dynamics, we find strong periodic modulations of the transmission and reflection envelopes in the scattered few-photon pulses, including photon compression and blockade, as well as dramatic changes in the quantum light statistics. Our theoretical analysis allows us to explain these non-trivial phenomena as arising from non-adiabatic memory effects.

quant-ph↗

arXiv2015

Quantum theory of light scattering in a one-dimensional channel: Interaction effect on photon statistics and entanglement entropy

We provide a complete and exact quantum description of coherent light scattering in a one-dimensional multi-mode transmission line coupled to a two-level emitter. Using recently developed scattering approach we discuss transmission properties, power spectrum, the full counting statistics and the entanglement entropy of transmitted and reflected states of light. Our approach takes into account spatial parameters of an incident coherent pulse as well as waiting and counting times of a detector. We describe time evolution of the power spectrum as well as observe deviations from the Poissonian statistics for reflected and transmitted fields. In particular, the statistics of reflected photons can change from sub-Poissonian to super-Poissonian for increasing values of the detuning, while the statistics of transmitted photons is strictly super-Poissonian in all parametric regimes. We study the entanglement entropy of some spatial part of the scattered pulse and observe that it obeys the area laws and that it is bounded by the maximal entropy of the effective four-level system.

quant-ph↗

arXiv2014

A tunable, nonlinear Hong-Ou-Mandel interferometer

We investigate the two-photon scattering properties of a Jaynes-Cummings (JC) nonlinearity consisting of a two-level system (qubit) interacting with a single mode cavity, which is coupled to two waveguides, each containing a single incident photon wave packet initially. In this scattering setup, we study the interplay between the Hong-Ou-Mandel effect arising due to quantum interference and effective photon-photon interactions induced by the presence of the qubit. We calculate the two-photon scattering matrix of this system analytically and identify signatures of interference and interaction in the second order auto- and cross-correlation functions of the scattered photons. In the dispersive regime, when qubit and cavity are far detuned from each other, we find that the JC nonlinearity can be used as an almost linear, in-situ tunable beam splitter giving rise to ideal Hong-Ou-Mandel interference, generating a highly path-entangled two-photon NOON state of the scattered photons. The latter manifests itself in strongly suppressed waveguide cross-correlations and Poissonian photon number statistics in each waveguide. If the two-level system and the cavity are on resonance, the JC nonlinearity strongly modifies the ideal HOM conditions leading to a smaller degree of path entanglement and sub-poissonian photon number statistics. In the latter regime, we find that photon blockade is associated with bunched auto-correlations in both waveguides, while a two-polariton resonance can lead to bunched as well as anti-bunched correlations.

quant-ph↗