Session AA02: V: Nonequilibrium Dynamics

Many-body localization transition in coupled incommensurate Heisenberg chains.

In this work, we report a quantum many-body localization (MBL) transition in a ladder formed by two coupled incommensurate spin chains with spin 1/2. The two chains are described by an isotropic Heisenberg model and are coupled to each other by quasi-periodic couplings that decay exponentially with the distance between sites. Using matrix product states (MPS), we study the time evolution of the bipartite entanglement entropy after a quantum quench. We show that the entanglement entropy follows a transition from volume law to area law scaling with increasing the incommensurate ratio of lattice parameters and the inter-chain exchange interaction strength. To characterize the MBL phase, we calculate the inverse participation ratio(IPR) using the exact diagonalization at zero net magnetization, which is extrapolated to the thermodynamic limit. We discuss the interpretation of the MBL transition in light of equivalent fermionic models.   

Decay rate of the generalized survival probability as a signature of localization transitions

The survival probability measures the probability that a system taken out of equilibrium remains in its initial state. It is given by the power spectrum of the energy distribution of the initial state, which is also known as the local density of states (LDOS). The width of the LDOS gives the short-time decay rate of the survival probability. Inspired by the generalized entropies, we introduce a generalized version of the survival probability. We show that the width of the generalized LDOS, σ_q , can be used to detect the transition from a phase with extended states to a localized phase. In contrast with existing quantities to detect this transition,  σ_q is self-averaging. Our studies are done for the following four systems: the power-law banded random matrix ensemble, the one-dimensional Aubry-Andr'e model with and without interactions, and the one-dimensional Heisenberg model with on-site disorder.   

Many-body scars in multiband Majorana fermion systems

In some quantum systems, the Hilbert space breaks up into a large ergodic sector and a smaller scar subspace. They may sometimes be distinguished by their transformation under a group whose rank grows with the system size. The quantum many-body scars are invariant under this group, while all other states are not. We apply this idea to lattice systems with N sites and M Majorana fermions per site. We identify two families of scars that are SO(N)-invariant. For M=4, where our construction reduces to spin-1/2 fermions, they are the eta-pairing states and the states of maximum spin. For M=6 we derive exact scar wavefunctions and entanglement entropy. It grows logarithmically with the sub-system size. We argue that any group-invariant scars generally have the entanglement entropy parametrically smaller than that of generic states. The scars energies are not equidistant in general but can be made so. With local Hamiltonians the scars typically have certain degeneracies. The scar spectrum can be made ergodic by adding a non-local interaction term. Because the number of scars grows exponentially with M, they make a sizable contribution to the density of states for small N.   

Periodically and quasiperiodically driven-anisotropic Dicke model

We analyze the anisotropic Dicke model in the presence of a periodic drive and under a quasiperiodic drive. The study of drive-induced phenomena in this experimentally accesible model is important since although it is simpler than full-fledged many-body quantum systems, it is still rich enough to exhibit many interesting features. We show that under a quasiperiodic Fibonacci (Thue-Morse) drive, the system features a prethermal plateau that increases as an exponential (stretched exponential) with the driving frequency before heating to an infinite-temperature state. In contrast, when the model is periodically driven, the dynamics reaches a plateau that is not followed by heating. In either case, the plateau value depends on the energy of the initial state and on the parameters of the undriven Hamiltonian. Surprisingly, this value does not always approach the infinite-temperature state monotonically as the frequency of the periodic drive decreases. We also show how the drive modifies the quantum critical point and discuss open questions associated with the analysis of level statistics at intermediate frequencies.   

Thermodynamics and fractal Drude weights in the sine-Gordon model

The sine-Gordon model is a paradigmatic quantum field theory that provides the low-energy effective description of many gapped 1D systems. Despite this fact, its complete thermodynamic description in all its regimes has been lacking. Here we fill this gap and derive the framework that captures its thermodynamics and serves as the basis of its hydrodynamic description. As a first application, we compute the Drude weight characterising the ballistic transport of topological charge and demonstrate that its dependence on the value of the coupling shows a fractal structure, similar to the gapless phase of the XXZ spin chain. The thermodynamic framework can be applied to study other features of non-equilibrium dynamics in the sine-Gordon model using generalised hydrodynamics, opening the way to a wide array of theoretical studies and potential novel experimental predictions.   

Symmetries as Ground States of Local Superoperators

Symmetry algebras of quantum many-body systems with locality can be understood using commutant algebras, which are defined as algebras of operators that commute with a given set of local operators. In this work, we show that these symmetry algebras can be expressed as frustration-free ground states of a local superoperator, which we refer to as a "super-Hamiltonian". We demonstrate that for conventional on-site unitary symmetries, the symmetry algebras map to various kinds of ferromagnetic ground states. We obtain a physical interpretation of this super-Hamiltonian as the superoperator that governs the operator relaxation in noisy symmetric Brownian circuits, which relates its low-energy excitations to approximate symmetries that determine slowly relaxing modes in symmetric systems. We find examples of gapped/gapless super-Hamiltonians indicating the absence/presence of slow-modes, which happens in the presence of discrete/continuous symmetries. In the gapless cases, we recover slow-modes such as diffusion in the presence of U(1) symmetry. We also demonstrate this framework for unconventional symmetries that lead to Hilbert space fragmentation and quantum many-body scars, which lead to novel kinds of slow-modes such as tracer diffusion and asymptotic quantum scars.   

Measurement-induced criticality in quasiperiodic modulated random hybrid circuits

The measurement-induced phase transition (MIPT) is an out-of-equilibrium phase transition separating entangling and disentangling quantum dynamics in hybrid quantum circuits, resulting from the competition between random unitary dynamics and local projective measurements. In this work, we study the stability of the MIPT in one dimension to quenched quasiperiodic (QP) modulations as captured in the context of equilibrium statistical mechanics by the Luck bound ν≥1/(1−β), for the correlation length exponent ν. Considering non-Pisot QP structures, characterized by unbounded fluctuations, allows us to tune the wandering exponent β to exceed the Luck bound and destabilize the MIPT. Through extensive numerical simulations of random Clifford circuits, we establish an RG-flow to a series of infinite-QP phase transitions and characterize the corresponding universal properties. In particular, we find a stretched exponential space-time scaling behavior with an activation exponent ψ=β and a correlation length exponent that saturates the Luck bound. Our findings agree with recent analytic mapping of the MIPT to ground state properties of the quantum Potts model in the replica limit.   

Engineering and understanding of Cayley (and hyperbolic) crystals with prescribed nonabelian dynamics

Recently, Hamiltonian dynamics over hyperbolic lattices has gained attention not only for its novel theoretical aspects as alternatives of standard Euclidean lattices but also for its potential applications in cQED, quantum information theory, topological protection of states and critical phenomena. Mathematically, it has been realized that such systems, together with the Euclidean ones, are just an instance of a much broader class dubbed Cayley crystals, whose lattice sites are elements of a group while the Hamiltonian hoppings determine a Cayley graph on it. For physical applications, however, it is very profitable to be able to engineer crystals starting from desired local properties so as to have an understanding on the transport of states and the scalability of observables. In this talk I will show how to identify the "nonabelian skeleton" of a crystal and, conversely, how to build Cayley crystals starting from a given scalable structure. When the latter is finite, the Hamiltonian dynamics on Cayley crystals, comprising both abelian and nonabelian eigenstates, can be fully understood and is essentially equivalent to that of Euclidean crystals, but with a more structured unit cell. Moreover, such engineering of crystals allows to characterize explicitly all possible periodic boundary conditions in a straightforward way and suggests a way to embed them in real space so that, experimentally, it will be much easier to realize them than, e.g. in the hyperbolic case, using Poincarè-disk-like embeddings.