Romain Vasseur

Lattice fusion rules and logarithmic operator product expansions

Abstract The interest in Logarithmic Conformal Field Theories (LCFTs) has been growing over the last few years thanks to recent developments coming from various approaches. A particularly fruitful point of view consists in considering lattice models as regularizations for such quantum field theories. The indecomposability then encountered in the representation theory of the corresponding finite-dimensional associative algebras exactly mimics the Virasoro indecomposable modules expected to arise in the continuum limit. In this paper, we study in detail the so-called Temperley–Lieb (TL) fusion functor introduced in physics by Read and Saleur [N. Read and H. Saleur, Associative-algebraic approach to logarithmic conformal field theories, Nucl. Phys. B 777 (2007) 316]. Using quantum group results, we provide rigorous calculations of the fusion of various TL modules at roots of unity cases. Our results are illustrated by many explicit examples relevant for physics. We discuss how indecomposability arises in the “lattice” fusion and compare the mechanisms involved with similar observations in the corresponding field theory. We also discuss the physical meaning of our lattice fusion rules in terms of indecomposable operator product expansions of quantum fields.

Nonequilibrium quantum dynamics and transport: from integrability to many-body localization

We review the non-equilibrium dynamics of many-body quantum systems after a quantum quench with spatial inhomogeneities, either in the Hamiltonian or in the initial state. We focus on integrable and many-body localized systems that fail to self-thermalize in isolation and for which the standard hydrodynamical picture breaks down. The emphasis is on universal dynamics, non-equilibrium steady states and new dynamical phases of matter, and on phase transitions far from thermal equilibrium. We describe how the infinite number of conservation laws of integrable and many-body localized systems lead to complex non-equilibrium states beyond the traditional dogma of statistical mechanics.

Indecomposability parameters in chiral logarithmic conformal field theory

Abstract Work of the last few years has shown that the key algebraic features of Logarithmic Conformal Field Theories (LCFTs) are already present in some finite lattice systems (such as the XXZ spin-1/2 chain) before the continuum limit is taken. This has provided a very convenient way to analyze the structure of indecomposable Virasoro modules and to obtain fusion rules for a variety of models such as (boundary) percolation etc. LCFTs allow for additional quantum numbers describing the fine structure of the indecomposable modules, and generalizing the ‘b-number’ introduced initially by Gurarie for the c = 0 case. The determination of these indecomposability parameters (or logarithmic couplings) has given rise to a lot of algebraic work, but their physical meaning has remained somewhat elusive. In a recent paper, a way to measure b for boundary percolation and polymers was proposed. We generalize this work here by devising a general strategy to compute matrix elements of Virasoro generators from the numerical analysis of lattice models and their continuum limit. The method is applied to XXZ spin-1/2 and spin-1 chains with open (free) boundary conditions. They are related to gl ( n + m | m ) and osp ( n + 2 m | 2 m ) -invariant superspin chains and to non-linear sigma models with supercoset target spaces. These models can also be formulated in terms of dense and dilute loop gas. We check the method in many cases where the results were already known analytically. Furthermore, we also confront our findings with a construction generalizing Gurarieʼs, where logarithms emerge naturally in operator product expansions to compensate for apparently divergent terms. This argument actually allows us to compute indecomposability parameters in any logarithmic theory. A central result of our study is the construction of a Kac table for the indecomposability parameters of the logarithmic minimal models LM ( 1 , p ) and LM ( p , p + 1 ) .

Symmetry constraints on many-body localization

We derive general constraints on the existence of many-body localized (MBL) phases in the presence of global symmetries, and show that MBL is not possible with symmetry groups that protect multiplets (e.g. all non-Abelian symmetry groups). Based on simple representation theoretic considerations, we derive general Mermin-Wagner-type principles governing the possible alternative fates of non-equilibrium dynamics in isolated, strongly disordered quantum systems. Our results rule out the existence of MBL symmetry protected topological phases with non-Abelian symmetry groups, as well as time-reversal symmetry protected electronic topological insulators, and in fact all fermion topological insulators and superconductors in the 10-fold way classification. Moreover, extending our arguments to systems with intrinsic topological order, we rule out MBL phases with non-Abelian anyons as well as certain classes of symmetry enriched topological orders.

Traffic jams and intermittent flows in microfluidic networks.

We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a nonlinear process: the particle current does not scale with the particle density even in the dilute limit where no particle collision occurs. We demonstrate that this nonlinear behavior stems from long-range hydrodynamic interactions. Importantly, we also establish that there exists a maximal current above which no stationary particle flow can be sustained. For higher current values, intermittent traffic jams form, thereby inducing the ejection of the particles from the initial path and the subsequent invasion of the network. Eventually, we put our findings in the broader context of the transport processes of driven particles in low dimension.

Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain

The anomalous nature of spin transport in the XXZ quantum spin chain has been a topic of theoretical interest for some time. Here, the integrability of the underlying dynamics leads to a ballistic component of the spin current, characterized by a spin Drude weight, which measures the degree of divergence of the zero-frequency spin conductivity. However, this quantity had previously proven to be beyond the reach of standard Bethe ansatz techniques. Here, the authors show that a recently developed hydrodynamic formalism for quantum integrable models may be used to compute the spin Drude weight. They also propose a numerical scheme to obtain hydrodynamic predictions for finite-time energy transport. This suggests that the hydrodynamic approach captures completely the ballistic component that dominates transport at long times and distances in the gapless regime of the XXZ model.

Resurrecting dead-water phenomenon

Abstract. We revisit experimental studies performed by Ekman on dead-water (Ekman, 1904) using modern techniques in order to present new insights on this peculiar phenomenon. We extend its description to more general situations such as a three-layer fluid or a linearly stratified fluid in presence of a pycnocline, showing the robustness of dead-water phenomenon. We observe large amplitude nonlinear internal waves which are coupled to the boat dynamics, and we emphasize that the modeling of the wave-induced drag requires more analysis, taking into account nonlinear effects. Dedicated to Fridtjof Nansen born 150 yr ago (10 October 1861).

A physical approach to the classification of indecomposable Virasoro representations from the blob algebra

Abstract In the context of Conformal Field Theory (CFT), many results can be obtained from the representation theory of the Virasoro algebra. While the interest in Logarithmic CFTs has been growing recently, the Virasoro representations corresponding to these quantum field theories remain dauntingly complicated, thus hindering our understanding of various critical phenomena. We extend in this paper the construction of Read and Saleur (2007) [1] , [2] , and uncover a deep relationship between the Virasoro algebra and a finite-dimensional algebra characterizing the properties of two-dimensional statistical models, the so-called blob algebra (a proper extension of the Temperley–Lieb algebra). This allows us to explore vast classes of Virasoro representations (projective, tilting, generalized staggered modules, etc.), and to conjecture a classification of all possible indecomposable Virasoro modules (with, in particular, L 0 Jordan cells of arbitrary rank) that may appear in a consistent physical Logarithmic CFT where Virasoro is the maximal local chiral algebra. As by-products, we solve and analyze algebraically quantum-group symmetric XXZ spin chains and sl ( 2 | 1 ) supersymmetric spin chains with extra spins at the boundary, together with the “mirror” spin chain introduced by Martin and Woodcock (2003) [3] .

Logarithmic observables in critical percolation

Although it has long been known that the proper quantum field theory description of critical percolation involves a logarithmic conformal field theory (LCFT), no direct consequence of this has been observed so far. Representing critical bond percolation as the Q = 1 limit of the Q-state Potts model, and analyzing the underlying S_Q symmetry of the Potts spins, we identify a class of simple observables whose two-point functions scale logarithmically for Q = 1. The logarithm originates from the mixing of the energy operator with a logarithmic partner that we identify as the field that creates two propagating clusters. In d=2 dimensions this agrees with general LCFT results, and in particular the universal prefactor of the logarithm can be computed exactly. We confirm its numerical value by extensive Monte-Carlo simulations.

Eigenstate phase transitions and the emergence of universal dynamics in highly excited states

We review recent advances in understanding the universal scaling properties of non-equilibrium phase transitions in non-ergodic disordered systems. We discuss dynamical critical points (also known as eigenstate phase transitions) between different many-body localized (MBL) phases, and between MBL and thermal phases.