Stron eigenstate thermalization hypothesis

We present a generalization of the ETH conjecture. Using this generalization we are able to derive the fact that an arbitrary eigenstate of a general many body system may be used to represent microcanonical ensemble in any many body experiment that involves only local operators and projectors onto eigenstates of the system Hamiltonian. In particular we extend the ETH to include some non-local operators. We present a derivation of this conjecture in the case of a many body model whose Hamiltonian is composed of two parts: an integrable Hamiltonian and a small but finite Gaussian perturbation.Comment: 4 pages, 1 figur

How to experimentally detect a GGE? - Universal Spectroscopic Signatures of the GGE in the Tonks gas

In this work we study the properties of the density density correlation function of the 1-D Lieb-Liniger model with infinite repulsion in the GGE regime. The GGE describes the equilibrated system in the long time limit after a quench from a generic initial state. In the case that the initial and hence the final state has low entropy per particle we find that the density density correlation function has a universal form, in particular it depends on a few parameters corresponding to "key" momenta and has power law dependence on the distance. This provides an experimental signature of the GGE which may readily be identified through spectroscopy. These signatures are universal and robust to initial sate preparation.Comment: 6 pages, 4 figure

Failure of the GGE hypothesis for integrable models with bound states

In this work we study the applicability of the GGE to integrable one dimensional systems with bound states. We find that the GGE fails to describe the long time dynamics for most initial states including eigenstates. We present our calculations studying the attractive Lieb-Liniger gas and the XXZ magnet, though similar results may be obtained for other models.Comment: 4 pages, 1 figur

Equilibration and Generalized GGE in the Lieb Liniger gas

We study the nonequilibrium properties of the one dimensional Lieb Liniger model in the finite repulsion regime. Introducing a new version of the Yudson representation applicable to finite size systems and appropriately taking the infinite volume limit we are able to study equilibration of the Lieb Liniger gas in the thermodynamic limit. We provide a formalism to compute various correlation functions for highly non equilibrium initial states. We are able to find explicit analytic expressions for the long time limit of the expectation of the density, density density and related correlation functions. We show that the gas equilibriates to a diagonal ensemble which we show is equivalent to a generalized version of the GGE for sufficiently simple correlation functions, which in particular include density correlations.Comment: 4+epsilon pages, 2 figur

Equilibration and GGE for hard wall boundary conditions

In this work we present an analysis of a quench for the repulsive Lieb-Liniger gas confined to a large box with hard wall boundary conditions. We study the time average of local correlation functions and show that both the quench action approach and the GGE formalism are applicable for the long time average of local correlation functions. We find that the time average of the system corresponds to an eigenstate of the Lieb-Liniger Hamiltonian and that this eigenstate is related to an eigenstate of a Lieb-Liniger Hamiltonian with periodic boundary conditions on an interval of twice the length and with twice as many particles (a doubled system). We further show that local operators with support far away from the boundaries of the hard wall have the same expectation values with respect to this eigenstate as corresponding operators for the doubled system. We present an example of a quench where the gas is initially confined in several moving traps and then released into a bigger container, an approximate description of the Newton cradle experiment. We calculate the time average of various correlation functions for long times after the quench.Comment: 10 pages, 1 figur

Driven-dissipative ising model: mean field solution

We study the fate of the Ising model and its universal properties when driven by a rapid periodic drive and weakly coupled to a bath at equilibrium. The far from equilibrium steady-state regime of the system is accessed by means of a Floquet mean field approach. We show that, depending on the details of the bath, the drive can strongly renormalize the critical temperature to higher temperatures, modify the critical exponents, or even change the nature of the phase transition from second to first order after the emergence of a tricritical point. Moreover, by judiciously selecting the frequency of the field and by engineering the spectrum of the bath, one can drive a ferromagnetic Hamiltonian to an antiferromagnetically ordered phase and vice-versa.Comment: 5 pages, 3 figure

Photo-induced superconductivity in semiconductors

We show that optically pumped semiconductors can exhibit superconductivity. We illustrate this phenomenon in the case of a two-band semiconductor tunnel-coupled to broad-band reservoirs and driven by a continuous wave laser. More realistically, we also show that superconductivity can be induced in a two-band semiconductor interacting with a broad-spectrum light source. We furthermore discuss the case of a three-band model in which the middle band replaces the broad-band reservoirs as the source of dissipation. In all three cases, we derive the simple conditions on the band structure, electron-electron interaction, and hybridization to the reservoirs that enable superconductivity. We compute the finite superconducting gap and argue that the mechanism can be induced through both attractive and repulsive interactions and is robust to high temperatures.Comment: 14 pages, 7 figure

Quantum Limits on Parameter Estimation

We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1-3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most experimentally accessible situations, where multiple rounds of measurements, auxiliary systems or external control of the evolution are available. The proof presented demonstrates the equivalence of these more general metrology procedures to the simplest optimal strategy for which the bound is proven: a single measurement of a two-level system interacting with a time-independent Hamiltonian.Comment: Submitted to New Journal of Physic

Steady-state superconductivity in electronic materials with repulsive interactions

We study the effect of laser driving on a minimal model for a hexagonal two-dimensional material with broken inversion symmetry. Through the application of circularly polarised light and coupling to a thermal free electron bath, the system is driven into a nonequilibrium steady state with asymmetric, nonthermal carrier populations in the two valleys. We show that, in this steady state, interband superconducting correlations between electrons can develop independent of the sign of the electron-electron interactions. We discuss how our results apply, for example, to transition metal dichalcogenides. This work opens the door to technological applications of superconductivity in a range of materials that were hitherto precluded from it.Comment: 5+7 pages, 3+1 figure

Generalised route to effective field theories for quantum systems with local constraints

Some of the exciting phenomena uncovered in strongly correlated systems in recent years - for instance quantum topological order, deconfined quantum criticality, and emergent gauge symmetries -- appear in systems in which the Hilbert space is effectively projected at low energies in a way that imposes local constraints on the original degrees of freedom. Cases in point include spin liquids, valence bond systems, dimer models, and vertex models. In this work, we use a slave boson description coupled to a large-$S$ path integral formulation to devise a generalised route to obtain effective field theories for such systems. We demonstrate the validity and capability of our approach by studying quantum dimer models and by comparing our results with the existing literature. Field-theoretic approaches to date are limited to bipartite lattices, they depend on a gauge-symmetric understanding of the constraint, and they lack generic quantitative predictive power for the coefficients of the terms that appear in the Lagrangians of these systems. Our method overcomes all these shortcomings and we show how the results up to quadratic order compare with the known height description of the square lattice quantum dimer model, as well as with the numerical estimate of the speed of light of the photon excitations on the diamond lattice. Finally, instanton considerations allow us to infer properties of the finite-temperature behaviour in two dimensions.Comment: 18 pages, 12 figure