The ground state phase diagram of the O(n) quantum spin chains with nearest neighbor interactions, for n≥$ or larger, shows two gapped phases separated by a critical point often referred to as the Reshetikhin point. One of the phases contains the SU(n) invariant -P^{(0)} model which has been analyzed using the Temperley-Lieb algebra and, more recently, by a random loop model. These works show...
An alternative title could have been « How to characterise coherences and fluctuations in diffusive out-of-equilibrium many-body quantum systems ? ».
In general, the difficulty to characterise non-equilibrium systems lies in the fact that there is no analog of the Boltzmann distribution to describe thermodynamic variables and their fluctuations. Over the last 20 years, however, it was...
We explain recent bounds on the quantum corrections to the (classical) Pekar approximation of the ground state energy of the Fröhlich polaron model in the strong coupling limit, and their consequence on the existence of excited states and the polaron's effective mass.
Anyons with a statistical phase parameter \alpha \in (0,2) are quasi-particles interpolating between bosons and fermions. For topological reasons, they only exist in a 1D or 2D world, ie as excitations of special 2D or 1D systems. There exists a main agreed-upon 2D model (equivalent to usual bosons or fermions carrying Aharonov-Bohm magnetic fluxes of intensity \alpha) but several 1D models....
We provide sufficient conditions such that the time evolution of a mesoscopic tight-binding open system with a local Hartree-Fock non-linearity converges to a self-consistent non-equilibrium steady state, which is independent of the initial condition from the "small sample". We also show that the steady charge current intensities are given by Landauer-Büttiker-like formulas, and make the...
I will review correlation inequalities for the two-point function of classical and quantum spin systems. These inequalities are “geometric” when they involve lattice sites. I will review the Simon-Lieb-Rivasseau, Messager-Miracle-Sole, and Lees-Taggi inequalities. I will point out that the Messager-Miracle-Sole inequalities can be extended to the spin-1/2 quantum XY model.
I will present results on the stability of the critical behavior of the 2D Ising Model and of
an interacting Weyl semimetal in presence of quasi-periodic disorder.
The analysis is based on fermionic RG combined with methods inspired by KAM theory.
We introduce a natural mathematical definition of boundary states of a bulk gapped ground state in the operator algebraic framework of 2-D quantum spin systems.
With the approximate Haag duality at the boundary, we derive a C*-tensor category M
out of such boundary state. Under a non-triviality condition of the braiding in the bulk, we show that the Drinfeld center (with an asymptotic...
The eigenstate thermalization hypothesis (ETH) was developed to explain the mechanism by which "chaotic" systems reach thermal equilibrium from a generic state. ETH is an ansatz for the matrix elements of physical operators in the basis of the Hamiltonian, and since its postulation, numerous studies have characterized these quantities in increasingly fine detail, providing a solid framework...
The talk concerns the correspondence between the topological triviality of gapped quantum systems and the existence of an orthonormal basis of well-localized Wannier functions spanning the range of the Fermi projection.
For periodic systems in dimension 2 and 3 such a correspondence has been noticed and proved, and dubbed Localization Dichotomy. Under general assumptions, it has been proved...
I will present some of our recent results concerning the dynamical fluctuations of single, classical or quantum, random walker on a lattice, subject to external continuous monitoring. Exploiting analogies with KPZ physics, I will show that these systems have non trivial scaling of their fluctuations and can exhibit a phase transition in dimensions higher than 1.
Motivated by understanding how temperature affects topological order, I will present some recent estimates for the mixing time of Davies dynamics in quantum spin systems.
Symmetries play a fundamental role in shaping physical theories, from quantum mechanics to thermodynamics. Studying the entropic, energetic, or dynamic signatures of underlying symmetries in quantum systems is an active field of research, from fundamental questions about entropy scalings, ground state properties, or thermalization, to the optimization of quantum computing or numerical...
In this talk I will formulate the problem of approach to equilibrium in algebraic quantum statistical mechanics and study some of its structural aspects, focusing on the relation between the zeroth law of thermodynamics (approach to equilibrium) and the second law (increase of entropy). The main result is that approach to equilibrium is necessarily accompanied by a strict increase of the...
We study the slowly varying, non-autonomous dynamics of a translation-invariant quantum spin system on the lattice Z^d . This system is assumed to be initially in thermal equilibrium, and we consider realizations of quasi-static processes in the adiabatic limit. By combining the Gibbs variational principle with the notion of quantum weak Gibbs states, we establish a number of general...
I will discuss how to represent the real-time dynamics of lattice fermionic systems exposed to slowly varying time-dependent perturbations in terms of Euclidean (i.e. imaginary time) correlation functions. The advantage is that, in many situations, time-ordered Euclidean correlation functions satisfy much better space-time decay estimates than their real-time counterparts. As an application, I...
Chiral spin liquids are topological-ordered states of matter, quantum spin analogs of the celebrated electronic Fractional Quantum Hall states. I will discuss how they can be represented in terms of tensor networks (despite a no-go theorem!). In a second step, I will discuss recent efforts for adiabatic preparation of such states using Floquet engineering.
We discuss a homogeneous system of interacting bosons in the mean-field regime where the temperature is comparable to the critical temperature for the Bose-Einstein condensation (BEC). By a rigorous implementation of Bogoliubov's approximation, we derive asymptotic formulas for the free energy and the reduced density matrices of the corresponding Gibbs state. In particular, our method allows...
The behavior of electrons in a metal presents a wide variety of emergent behavior including a number of phase transitions. The mean-field scaling limit acts as a simplified model capturing part of this complexity. In this limit, results going beyond the precision of Hartree-Fock theory have recently been obtained by bosonization methods. I will review the expansion of the ground state energy...