Garry Goldstein

Failure of the local generalized Gibbs ensemble for integrable models with bound states

In this work we study the applicability of the local GGE to integrable one dimensional systems with bound states. We find that the GGE, when defined using only local conserved quantities, 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.

Decay rates for topological memories encoded with Majorana fermions

Recently there have been numerous proposals to create Majorana zero modes in solid state heterojunctions, superconducting wires and optical lattices. Putatively the information stored in qubits constructed from these modes is protected from various forms of decoherence. Here we show that this is not the case. We present a generic method to study the effect of external perturbations on these modes. We focus on the case where there are no interactions between different Majorana modes either directly or through intermediary fermions. To quantify the rate of loss of the information stored in the Majorana modes we study the two-time correlators for qubits built from them. We analyze a generic gapped fermionic environment (bath) interacting via tunneling with different components of the qubit (different Majorana modes). We find that static (time-independent) perturbations are not harmful, and just lead to a depletion of the information stored that saturates in the long-time limit. On the other hand we find markedly different results for dynamic (time dependent) systems, with no coherence surviving in the long time limit. In particular we find that dephasing and energy fluctuations of the modes in the fermionic bath have adverse effects on the Majorana memories.

Equilibration and generalized Gibbs ensemble 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.

Exact Zero Modes in Closed Systems of Interacting Fermions

We show that for closed finite sized systems with an odd number of real fermionic modes, even in the presence of interactions, there are always at least two fermionic operators that commute with the Hamiltonian.There is a zero mode corresponding to the fermion parity operator, as shown by Akhmerov, as well as additional linearly independent zero modes, one of which is 1) the one that is continuously connected to the Majorana mode solution in the non-interacting limit, and 2) less prone to decoherence when the system is opened to contact with an infinite bath. We also show that in the idealized situation where there are two or more well separated zero modes each associated with a finite number of fermions at a localized vortex, these modes have non-Abelian Ising statistics under braiding. Furthermore the algebra of the zero mode operators makes them useful for fermionic quantum computation.

d -wave superconductivity in boson+fermion dimer models

We present a slave-particle mean-field study of the mixed boson+fermion quantum dimer model introduced by Punk, Allais, and Sachdev [PNAS 112, 9552 (2015)] to describe the physics of the pseudogap phase in cuprate superconductors. Our analysis naturally leads to four charge e fermion pockets whose total area is equal to the hole doping p, for a range of parameters consistent with the t-J model for high temperature superconductivity. Here we find that the dimers are unstable to d-wave superconductivity at low temperatures. The region of the phase diagram with d-wave rather than s-wave superconductivity matches well with the appearance of the four fermion pockets. In the superconducting regime, the dispersion contains eight Dirac cones along the diagonals of the Brillouin zone.

Quench between a Mott insulator and a Lieb-Liniger liquid

In this work we study a quench between a Mott insulator and a repulsive Lieb-Liniger liquid. We find explicitly the stationary state when a long time has passed after the quench. It is given by a GGE density matrix which we completely characterize, calculating the quasiparticle density describing the system after the quench. In the long time limit we find an explicit form for the local three body density density density correlation function and the asymptotic long distance limit of the density density correlation function. The later is shown to have a Gaussian decay at large distances.

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 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.

Band-edge superconductivity

We show that superconductivity can arise in semiconductors with a band in the shape of a Mexican hat when the chemical potential is tuned close to the band edge, but not intersecting the band, as long as interactions are sufficiently strong. Hence, this is an example where superconductivity can emerge from a band insulator when interactions exceed a threshold. Semiconductors with simple cubic symmetry point groups and with strong spin-orbit coupling provide an example of a system with such band dispersion.

Photoinduced 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.