arXiv subjects

V. Gritsev

Publications and source records attributed to V. Gritsev.

At least 19 recordsLinked to original sources

arXiv2024

Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems

Topological insulators have been studied intensively over the last decades. Earlier research focused on Hermitian Hamiltonians, but recently, peculiar and interesting properties were found by introducing non-Hermiticity. In this work, we apply a quantum geometric approach to various Hermitian and non-Hermitian versions of the Su-Schrieffer-Heeger (SSH) model. We find that this method allows one to correctly identify different topological phases and topological phase transitions for all SSH models, but only when using the metric tensor containing both left and right eigenvectors. Whereas the quantum geometry of Hermitian systems is Riemannian, introducing non-Hermiticity leads to pseudo-Riemannian and complex geometries, thus significantly generalizing from the quantum geometries studied thus far. One remarkable example of this is the mathematical agreement between topological phase transition curves and lightlike paths in general relativity, suggesting a possibility of simulating space-times in non-Hermitian systems. We find that the metric in non-Hermitian phases degenerates in such a way that it effectively reduces the dimensionality of the quantum geometry by one. This implies that within linear response theory, one can perturb the system by a particular change of parameters while maintaining a zero excitation rate.

cond-mat.stat-mech↗

arXiv2023

Disordered impenetrable two-component fermions in one dimension

We study the one-dimensional Hubbard model for two-component fermions with infinitely strong on-site repulsion (t-0 model) in the presence of disorder. Our analytical treatment demonstrates that the type of disorder drastically changes the nature of the emerging phases. The case of spin-independent disorder can be treated as a single-particle problem with Anderson localization. On the contrary, recent numerical findings show that spin-dependent disorder, which can be realized as a random magnetic field, leads to the many-body localization-delocalization transition. We find an explicit analytic expression for the matrix elements of the random magnetic field between the eigenstates of the t-0 model with potential disorder on a finite lattice. Analysis of the matrix elements supports the existence of the many-body localization-delocalization transition in this system and provides an extended physical picture of the random magnetic field.

cond-mat.dis-nn↗

arXiv2022

The spectral form factor in the `t Hooft limit -- Intermediacy versus universality

The Spectral Form Factor (SFF) is a convenient tool for the characterization of eigenvalue statistics of systems with discrete spectra, and thus serves as a proxy for quantum chaoticity. This work presents an analytical calculation of the SFF of the Chern-Simons Matrix Model (CSMM), which was first introduced to describe the intermediate level statistics of disordered electrons at the mobility edge. The CSMM is characterized by a parameter $ 0 \leq q\leq 1$, where the Circular Unitary Ensemble (CUE) is recovered for $q\to 0$. The CSMM was later found as a matrix model description of $U(N)$ Chern-Simons theory on $S^3$, which is dual to a topological string theory characterized by string coupling $g_s=-\log q$. The spectral form factor is proportional to a colored HOMFLY invariant of a $(2n,2)$-torus link with its two components carrying the fundamental and antifundamental representations, respectively. We check that taking $N \to \infty$ whilst keeping $q<1$ reduces the connected SFF to an exact linear ramp of unit slope, confirming the main result from arXiv:2012.11703 for the specific case of the CSMM. We then consider the `t Hooft limit, where $N \to \infty$ and $q \to 1^-$ such that $y = q^N $ remains finite. As we take $q\to 1^-$, this constitutes the opposite extreme of the CUE limit. In the `t Hooft limit, the connected SFF turns into a remarkable sequence of polynomials which, as far as the authors are aware, have not appeared in the literature thus far. A gap opens in the spectrum and, after unfolding by a constant rescaling, the connected SFF approximates a linear ramp of unit slope for all $y$ except $y \approx 1$, where the connected SFF goes to zero. We thus find that, although the CSMM was introduced to describe intermediate statistics and the `t Hooft limit is the opposite limit of the CUE, we still recover Wigner-Dyson universality for all $y$ except $y\approx 1$.

cond-mat.str-el↗

arXiv2022

Driven-dissipative time crystalline phases in a two-mode bosonic system with Kerr nonlinearity

For the driven-dissipative system of two coupled bosonic modes in a nonlinear cavity resonator, we demonstrate a sequence of phase transitions from a trivial steady state to two distinct dissipative time crystalline phases. These effects are already anticipated at the level of the semiclassical analysis of the Lindblad equation using the theory of bifurcations and are further supported by the full quantum (numerical) treatment. The system is predicted to exhibit different dynamical phases characterized by an oscillating non-equilibrium steady state with non-trivial periodicity, which is a hallmark of time crystals. We expect that these phases can be directly probed in various cavity QED experiments.

quant-ph↗

arXiv2022

Floquet integrability and long-range entanglement generation in the one-dimensional quantum Potts model

We develop a Floquet protocol for long-range entanglement generation in the one-dimensional quantum Potts model, which generalizes the transverse-filed Ising model by allowing each spin to have $n>2$ states. We focus on the case of $n=3$, so that the model describes a chain of qutrits. The suggested protocol creates qutrit Bell-like pairs with non-local long-range entanglement that spans over the entire chain. We then conjecture that the proposed Floquet protocol is integrable and explicitly construct a few first non-trivial conserved quantities that commute with the stroboscopic evolution operator. Our analysis of the Floquet integrability relies on the deep connection between the quantum Potts model and a much broader class of models described by the Temperley-Lieb algebra. We work at the purely algebraic level and our results on Floquet integrability are valid for any representation of the Temperley-Lieb algebra. We expect that our findings can be probed with present experimental facilities using Rydberg programmable quantum simulators and can find various applications in quantum technologies.

cond-mat.quant-gas↗

arXiv2022

Free Fock parafermions in the tight-binding model with dissipation

Parafermions that generalize (Majorana or usual) fermions appear as interacting quasi-particles because of their nature. Although attempts to develop models with free (non-interacting) parafermions have been undertaken, existing proposals require unphysical conditions such as realizing purely non-Hermitian systems. Here we present a way for the realization of free Fock parafermions in the tight-binding model with controlled dissipation of a very simple form. Introducing dissipation transforms an originally non-integrable quantum model to an exactly solvable classical one.

cond-mat.quant-gas↗

arXiv2020

Lie-algebraic approach to one-dimensional translationally invariant free-fermionic dissipative systems

We study dissipative translationally invariant free-fermionic theories with quadratic Liouvillians. Using a Lie-algebraic approach, we solve the Lindblad equation and find the density matrix at all times for arbitrary time dependence of the Liouvillian. We then investigate the Liouvillian spectral properties and derive a generic criterion for the closure of the dissipative gap, which is believed to be linked with nonequilibrium dissipative phase transitions. We illustrate our findings with a few exotic examples. Particularly, we show the presence of gapless modes with a linear spectrum for fermions with long-range hopping, which might be related to nonunitary conformal field theories. The predicted effects can be probed in experiments with ultracold atomic and quantum-optical systems using currently available experimental facilities.

quant-ph↗

arXiv2020

Simulating a quantum commensurate-incommensurate phase transition using two Raman coupled one dimensional condensates

We study a transition between a homogeneous and an inhomogeneous phase in a system of one-dimensional, Raman tunnel-coupled Bose gases. The homogeneous phase shows a flat density and phase profile, whereas the inhomogeneous ground state is characterized by periodic density ripples, and a soliton staircase in the phase difference. We show that under experimentally viable conditions the transition can be tuned by the wavevector difference $Q$ of the Raman beams and can be described by the Pokrovsky-Talapov model for the relative phase between the two condensates. Local imaging available in atom chip experiments allows to observe the soliton lattice directly, while modulation spectroscopy can be used to explore collective modes, such as the phonon mode arising from breaking of translation symmetry by the soliton lattice. In addition, we investigate regimes where the cold atom experiment deviates from the Pokrovsky-Talapov field theory. We predict unusual mesoscopic effects arising from the finite size of the system, such as quantized injection of solitons upon increasing $Q$, or the system size. For moderate values of $Q$ above criticality, we find that the density modulations in the two gases interplay with the relative phase profile and introduce novel features in the spatial structure of the mode wave-functions. Using an inhomogeneous Bogoliubov theory, we show that spatial quantum fluctuations are intertwined with the emerging soliton staircase. Finally, we comment on the prospects of the ultra-cold atom setup as a tunable platform studying quantum aspects of the Pokrovsky-Talapov theory in and out-of-equilibrium.

cond-mat.quant-gas↗

arXiv2018

One-dimensional two-component fermions with contact even-wave repulsion and SU(2) breaking near-resonant odd-wave attraction

We consider a one-dimensional (1D) two-component atomic Fermi gas with contact interaction in the even-wave channel (Yang-Gaudin model) and study the effect of an SU(2) symmetry breaking near-resonant odd-wave interaction within one of the components. Starting from the microscopic Hamiltonian, we derive an effective field theory for the spin degrees of freedom using the bosonization technique. It is shown that at a critical value of the odd-wave interaction there is a first-order phase transition from a phase with zero total spin and zero magnetization to the spin-segregated phase where the magnetization locally differs from zero.

cond-mat.quant-gas↗

arXiv2012

Dynamical Quantum Hall Effect in the Parameter Space

Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase (M.V. Berry (1984), Proc. Royal. Soc. London A, 392:45) which naturally emerges in quantum adiabatic evolution. So far the applicability and measurements of the Berry phase were mostly limited to systems of weakly interacting quasi-particles, where interference experiments are feasible. Here we show how one can go beyond this limitation and observe the Berry curvature and hence the Berry phase in generic systems as a non-adiabatic response of physical observables to the rate of change of an external parameter. These results can be interpreted as a dynamical quantum Hall effect in a parameter space. The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. We observe the quantization of this response, which term the rotational quantum Hall effect.

cond-mat.stat-mech↗

arXiv2010

Quench dynamics near a quantum critical point: application to the sine-Gordon model

We discuss the quench dynamics near a quantum critical point focusing on the sine-Gordon model as a primary example. We suggest a unified approach to sudden and slow quenches, where the tuning parameter $λ(t)$ changes in time as $λ(t)\sim \upsilon t^r$, based on the adiabatic expansion of the excitation probability in powers of $\upsilon$. We show that the universal scaling of the excitation probability can be understood through the singularity of the generalized adiabatic susceptibility $χ_{2r+2}(λ)$, which for sudden quenches ($r=0$) reduces to the fidelity susceptibility. In turn this class of susceptibilities is expressed through the moments of the connected correlation function of the quench operator. We analyze the excitations created after a sudden quench of the cosine potential using a combined approach of form-factors expansion and conformal perturbation theory for the low-energy and high-energy sector respectively. We find the general scaling laws for the probability of exciting the system, the density of excited quasiparticles, the entropy and the heat generated after the quench. In the two limits where the sine-Gordon model maps to hard core bosons and free massive fermions we provide the exact solutions for the quench dynamics and discuss the finite temperature generalizations.

cond-mat.other↗

arXiv2009

Quench dynamics near a quantum critical point

We study the dynamical response of a system to a sudden change of the tuning parameter $λ$ starting (or ending) at the quantum critical point. In particular we analyze the scaling of the excitation probability, number of excited quasiparticles, heat and entropy with the quench amplitude and the system size. We extend the analysis to quenches with arbitrary power law dependence on time of the tuning parameter, showing a close connection between the scaling behavior of these quantities with the singularities of the adiabatic susceptibilities of order $m$ at the quantum critical point, where $m$ is related to the power of the quench. Precisely for sudden quenches the relevant susceptibility of the second order coincides with the fidelity susceptibility. We discuss the generalization of the scaling laws to the finite temperature quenches and show that the statistics of the low-energy excitations becomes important. We illustrate the relevance of those results for cold atoms experiments.

cond-mat.stat-mech↗

arXiv2009

Density ripples in expanding low-dimensional gases as a probe of correlations

We investigate theoretically the evolution of the two-point density correlation function of a low-dimensional ultracold Bose gas after release from a tight transverse confinement. In the course of expansion thermal and quantum fluctuations present in the trapped systems transform into density fluctuations. For the case of free ballistic expansion relevant to current experiments, we present simple analytical relations between the spectrum of ``density ripples'' and the correlation functions of the original confined systems. We analyze several physical regimes, including weakly and strongly interacting one-dimensional (1D) Bose gases and two-dimensional (2D) Bose gases below the Berezinskii-Kosterlitz-Thouless (BKT) transition. For weakly interacting 1D Bose gases, we obtain an explicit analytical expression for the spectrum of density ripples which can be used for thermometry. For 2D Bose gases below the BKT transition, we show that for sufficiently long expansion times the spectrum of the density ripples has a self-similar shape controlled only by the exponent of the first-order correlation function. This exponent can be extracted by analyzing the evolution of the spectrum of density ripples as a function of the expansion time.

cond-mat.quant-gas↗

arXiv2008

Interferometric probe of paired states

We propose a new method for detecting paired states in either bosonic or fermionic systems using interference experiments with independent or weakly coupled low dimensional systems. We demonstrate that our method can be used to detect both the FFLO and the d-wave paired states of fermions, as well as quasicondensates of singlet pairs for polar F=1 atoms in two dimensional systems. We discuss how this method can be used to perform phase-sensitive determination of the symmetry of the pairing amplitude.

cond-mat.other↗

arXiv2008

Probing quantum and thermal noise in an interacting many-body system

The probabilistic character of the measurement process is one of the most puzzling and fascinating aspects of quantum mechanics. In many-body systems quantum mechanical noise reveals non-local correlations of the underlying many-body states. Here, we provide a complete experimental analysis of the shot-to-shot variations of interference fringe contrast for pairs of independently created one-dimensional Bose condensates. Analyzing different system sizes we observe the crossover from thermal to quantum noise, reflected in a characteristic change in the distribution functions from Poissonian to Gumbel-type, in excellent agreement with theoretical predictions based on the Luttinger liquid formalism. We present the first experimental observation of quasi long-range order in one-dimensional atomic condensates, which is a hallmark of quantum fluctuations in one-dimensional systems. Furthermore, our experiments constitute the first analysis of the full distribution of quantum noise in an interacting many-body system.

cond-mat.other↗

arXiv2008

Breakdown of the adiabatic limit in low dimensional gapless systems

It is generally believed that a generic system can be reversibly transformed from one state into another by sufficiently slow change of parameters. A standard argument favoring this assertion is based on a possibility to expand the energy or the entropy of the system into the Taylor series in the ramp speed. Here we show that this argumentation is only valid in high enough dimensions and can break down in low-dimensional gapless systems. We identify three generic regimes of a system response to a slow ramp: (A) mean-field, (B) non-analytic, and (C) non-adiabatic. In the last regime the limits of the ramp speed going to zero and the system size going to infinity do not commute and the adiabatic process does not exist in the thermodynamic limit. We support our results by numerical simulations. Our findings can be relevant to condensed-matter, atomic physics, quantum computing, quantum optics, cosmology and others.

cond-mat.stat-mech↗

arXiv2007

Crystallization of strongly interacting photons in a nonlinear optical fiber

Understanding strongly correlated quantum systems is a central problem in many areas of physics. The collective behavior of interacting particles gives rise to diverse fundamental phenomena such as confinement in quantum chromodynamics, phase transitions, and electron fractionalization in the quantum Hall regime. While such systems typically involve massive particles, optical photons can also interact with each other in a nonlinear medium. In practice, however, such interactions are often very weak. Here we describe a novel technique that allows the creation of a strongly correlated quantum gas of photons using one-dimensional optical systems with tight field confinement and coherent photon trapping techniques. The confinement enables the generation of large, tunable optical nonlinearities via the interaction of photons with a nearby cold atomic gas. In its extreme, we show that a quantum light field can undergo fermionization in such one-dimensional media, which can be probed via standard photon correlation measurements.

cond-mat.other↗

arXiv2007

Dynamical instability of the XY spiral state of ferromagnetic condensates

We calculate the spectrum of collective excitations of the XY spiral state prepared adiabatically or suddenly from a uniform ferromagnetic F=1 condensate. For spiral wavevectors past a critical value, spin wave excitation energies become imaginary indicating a dynamical instability. We construct phase diagrams as functions of spiral wavevector and quadratic Zeeman energy.

cond-mat.other↗