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We consider Glauber dynamics of classical spin systems of Ising type in the limit when the temperature tends to zero in finite volume. We show that information on the structure of the most profound minima and the connecting saddle points of…
We investigate means to describe the non-local properties of quantum systems and to test if two quantum systems are locally equivalent. For this we consider quantum systems that consist of several subsystems, especially multiple qubits. We…
The nonrelativistic limit of nonlocal modifications to the Klein Gordon operator is studied, and the experimental possibilities of casting stringent constraints on the nonlocality scale via planned and/or current optomechanical experiments…
We study in detail the properties of the quantum East model, an interacting quantum spin chain inspired by simple kinetically-constrained models of classical glasses. Through a combination of analytics, exact diagonalization and…
We study complexity of several problems related to the Transverse field Ising Model (TIM). First, we consider the problem of estimating the ground state energy known as the Local Hamiltonian Problem (LHP). It is shown that the LHP for TIM…
Let $B$, $I$ be the unweighted backward shift and the identity operator respectively on $l^{\infty}(\mathbb{N})$, the space of bounded sequences over the complex numbers endowed with the supremum norm. We prove that $I+\lambda B$ is locally…
Eigenstate thermalization is widely accepted as the mechanism behind thermalization in generic isolated quantum systems. Using the example of a single magnetic defect embedded in the integrable spin-1/2 $XXZ$ chain, we show that locally…
Eigenstate Thermalization Hypothesis provides one picture of thermalization in a quantum system by looking at individual eigenstates. However, it is also important to consider how local observables reach equilibrium values dynamically.…
We establish a rigorous relation between the thermalization of typical initial states and the dynamics of local operators. We introduce a concept of simple slow operators (SSOs), defined as operators that have a small commutator with the…
We investigate the relation between transport properties and entanglement between the internal (spin) and external (position) degrees of freedom in one-dimensional discrete time quantum walks. We obtain closed-form expressions for the…
A general scalar-tensor theory can be formulated in different parametrizations that are related by a conformal rescaling of the metric and a scalar field redefinition. We compare formulations of slow-roll regimes in the Einstein and Jordan…
We investigate the topological-to-non-topological quantum phase transitions (QPTs) occurring in the Kitaev code under local perturbations in the form of local magnetic field and spin-spin interactions of the Ising-type using fidelity…
For random quantum spin models, the strong disorder perturbative expansion of the Local Integrals of Motion (LIOMs) around the real-spin operators is revisited. The emphasis is on the links with other properties of the Many-Body-Localized…
The study by Glauber of the time-dependent statistics of the Ising chain is extended to the case where each spin is influenced unequally by its nearest neighbours. The asymmetry of the dynamics implies the failure of the detailed balance…
Quantum systems can exhibit a great deal of universality at low temperature due to the structure of ground states and the critical points separating distinct states. On the other hand, quantum time evolution of the same systems involves all…
A delocalization phenomenon is studied in a class of non-Hermitian random quantum-mechanical problems. Delocalization arises in response to a sufficiently large constant imaginary vector potential. The transition is related to depinning of…
We consider in parallel three one-dimensional spin models with kinetic constraints: the paramagnetic constrained Ising chain, the ferromagnetic Ising chain with constrained Glauber dynamics, and the same chain with constrained Kawasaki…
Understanding the asymptotic behavior of physical quantities in the thermodynamic limit is a fundamental problem in statistical mechanics. In this paper, we study how fast the eigenstate expectation values of a local operator converge to a…
We investigate the entanglement and nonlocality properties of two random XX spin-1/2 critical chains, in order to better understand the role of breaking translational invariance to achieve nonlocal states in critical systems. We show that…
We apply the linked cluster expansion as well as the quench action approach to study the time evolution of one-point functions after a quantum quench in integrable field theories. We argue that the relaxation towards the stationary value…