120 research outputs found
Aspects of Confinement in Low Dimensions
We briefly review some examples of confinement which arise in condensed
matter physics. We focus on two instructive cases: the off-critical Ising model
in a magnetic field, and an array of weakly coupled (extended) Hubbard chains
in the Wigner crystal phase. In the appropriate regime, the elementary
excitations in these 1+1 and quasi-one-dimensional systems are confined into
`mesons'. Although the models are generically non-integrable, quantum mechanics
and form factor techniques yield valuable information.Comment: Contribution to Ian Kogan memorial volume, World Scientifi
Feshbach Resonance in Optical Lattices and the Quantum Ising Model
Motivated by experiments on heteronuclear Feshbach resonances in Bose
mixtures, we investigate s-wave pairing of two species of bosons in an optical
lattice. The zero temperature phase diagram supports a rich array of superfluid
and Mott phases and a network of quantum critical points. This topology reveals
an underlying structure that is succinctly captured by a two-component Landau
theory. Within the second Mott lobe we establish a quantum phase transition
described by the paradigmatic longitudinal and transverse field Ising model.
This is confirmed by exact diagonalization of the 1D bosonic Hamiltonian. We
also find this transition in the homonuclear case.Comment: 5 pages, 4 figure
Quantum Phase Transitions in Bosonic Heteronuclear Pairing Hamiltonians
We explore the phase diagram of two-component bosons with Feshbach resonant
pairing interactions in an optical lattice. It has been shown in previous work
to exhibit a rich variety of phases and phase transitions, including a
paradigmatic Ising quantum phase transition within the second Mott lobe. We
discuss the evolution of the phase diagram with system parameters and relate
this to the predictions of Landau theory. We extend our exact diagonalization
studies of the one-dimensional bosonic Hamiltonian and confirm additional Ising
critical exponents for the longitudinal and transverse magnetic
susceptibilities within the second Mott lobe. The numerical results for the
ground state energy and transverse magnetization are in good agreement with
exact solutions of the Ising model in the thermodynamic limit. We also provide
details of the low-energy spectrum, as well as density fluctuations and
superfluid fractions in the grand canonical ensemble.Comment: 11 pages, 14 figures. To appear in Phys. Rev.
Non-equilibrium steady states in the Klein-Gordon theory
We construct non-equilibrium steady states in the Klein-Gordon theory in
arbitrary space dimension following a local quench. We consider the
approach where two independently thermalized semi-infinite systems, with
temperatures and , are connected along a
-dimensional hypersurface. A current-carrying steady state, described by
thermally distributed modes with temperatures and for
left and right-moving modes, respectively, emerges at late times. The
non-equilibrium density matrix is the exponential of a non-local conserved
charge. We obtain exact results for the average energy current and the complete
distribution of energy current fluctuations. The latter shows that the
long-time energy transfer can be described by a continuum of independent
Poisson processes, for which we provide the exact weights. We further describe
the full time evolution of local observables following the quench. Averages of
generic local observables, including the stress-energy tensor, approach the
steady state with a power-law in time, where the exponent depends on the
initial conditions at the connection hypersurface. We describe boundary
conditions and special operators for which the steady state is reached
instantaneously on the connection hypersurface. A semiclassical analysis of
freely propagating modes yields the average energy current at large distances
and late times. We conclude by comparing and contrasting our findings with
results for interacting theories and provide an estimate for the timescale
governing the crossover to hydrodynamics. As a modification of our Klein-Gordon
analysis we also include exact results for free Dirac fermions.Comment: 42 pages, 7 figure
Magnetic Properties of the Second Mott Lobe in Pairing Hamiltonians
We explore the Mott insulating state of single-band bosonic pairing
Hamiltonians using analytical approaches and large scale density matrix
renormalization group calculations. We focus on the second Mott lobe which
exhibits a magnetic quantum phase transition in the Ising universality class.
We use this feature to discuss the behavior of a range of physical observables
within the framework of the 1D quantum Ising model and the strongly anisotropic
Heisenberg model. This includes the properties of local expectation values and
correlation functions both at and away from criticality. Depending on the
microscopic interactions it is possible to achieve either antiferromagnetic or
ferromagnetic exchange interactions and we highlight the possibility of
observing the E8 mass spectrum for the critical Ising model in a longitudinal
magnetic field.Comment: 14 pages, 15 figure
Collective Dynamics of Bose--Einstein Condensates in Optical Cavities
Recent experiments on Bose--Einstein condensates in optical cavities have
reported a quantum phase transition to a coherent state of the matter-light
system -- superradiance. The time dependent nature of these experiments demands
consideration of collective dynamics. Here we establish a rich phase diagram,
accessible by quench experiments, with distinct regimes of dynamics separated
by non-equilibrium phase transitions. We include the key effects of cavity
leakage and the back-reaction of the cavity field on the condensate. Proximity
to some of these phase boundaries results in critical slowing down of the decay
of many-body oscillations. Notably, this slow decay can be assisted by large
cavity losses. Predictions include the frequency of collective oscillations, a
variety of multi-phase co-existence regions, and persistent optomechanical
oscillations described by a damped driven pendulum. These findings open new
directions to study collective dynamics and non-equilibrium phase transitions
in matter-light systems.Comment: 5 pages, 5 figure
Non-equilibrium quantum spin dynamics from classical stochastic processes
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide exact formulae of broad applicability for the time-dependence of expectation values and correlation functions following a quantum quench in terms of averages over classical stochastic processes. We further explore the behavior of the classical stochastic variables in the presence of dynamical quantum phase transitions, including results for their distributions and correlation functions. We provide details on the numerical solution of the associated stochastic differential equations, and examine the growth of fluctuations in the classical description. We discuss the strengths and limitations of the current implementation of the stochastic approach and the potential for further development
Stochastic Approach to Non-Equilibrium Quantum Spin Systems
We investigate a stochastic approach to non-equilibrium quantum spin systems
based on recent insights linking quantum and classical dynamics. Exploiting a
sequence of exact transformations, quantum expectation values can be recast as
averages over classical stochastic processes. We illustrate this approach for
the quantum Ising model by extracting the Loschmidt amplitude and the
magnetization dynamics from the numerical solution of stochastic differential
equations. We show that dynamical quantum phase transitions are accompanied by
clear signatures in the associated classical distribution functions, including
the presence of enhanced fluctuations. We demonstrate that the method is
capable of handling integrable and non-integrable problems in a unified
framework, including those in higher dimensions.Comment: 5 pages, 5 figure
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