185 research outputs found
Strong and weak thermalization of infinite non-integrable quantum systems
When a non-integrable system evolves out of equilibrium for a long time,
local observables are expected to attain stationary expectation values,
independent of the details of the initial state. However, intriguing
experimental results with ultracold gases have shown no thermalization in
non-integrable settings, triggering an intense theoretical effort to decide the
question. Here we show that the phenomenology of thermalization in a quantum
system is much richer than its classical counterpart. Using a new numerical
technique, we identify two distinct thermalization regimes, strong and weak,
occurring for different initial states. Strong thermalization, intrinsically
quantum, happens when instantaneous local expectation values converge to the
thermal ones. Weak thermalization, well-known in classical systems, happens
when local expectation values converge to the thermal ones only after time
averaging. Remarkably, we find a third group of states showing no
thermalization, neither strong nor weak, to the time scales one can reliably
simulate.Comment: 12 pages, 21 figures, including additional materia
Indirect CP Violation in the B-System
We show that, contrary to the flavour mixing amplitude q/p, both Re(epsilon)
and Im(epsilon) are observable quantities, where epsilon is the phase-
convention-independent CP mixing. We consider semileptonic B_d decays from a CP
tag and build appropriate time-dependent asymmetries to separate out
Re(epsilon) and Im(epsilon). "Indirect" CP violation would have in
Im(epsilon)/(1+|epsilon|^2) its most prominent manifestation in the B-system,
with expected values in the standard model ranging from -0.37 to -0.18. This
quantity is controlled by a new observable phase: the relative one between the
CP-violating and CP-conserving parts of the effective hamiltonian. For
time-integrated rates we point out a (Delta Gamma)--> (Sigma Gamma)
transmutation which operates in the perturbative CP mixing.Comment: 7 pages, No figure
Thermal evolution of the Schwinger model with Matrix Product Operators
We demonstrate the suitability of tensor network techniques for describing
the thermal evolution of lattice gauge theories. As a benchmark case, we have
studied the temperature dependence of the chiral condensate in the Schwinger
model, using matrix product operators to approximate the thermal equilibrium
states for finite system sizes with non-zero lattice spacings. We show how
these techniques allow for reliable extrapolations in bond dimension, step
width, system size and lattice spacing, and for a systematic estimation and
control of all error sources involved in the calculation. The reached values of
the lattice spacing are small enough to capture the most challenging region of
high temperatures and the final results are consistent with the analytical
prediction by Sachs and Wipf over a broad temperature range.Comment: 6 pages, 11 figure
Variational study of U(1) and SU(2) lattice gauge theories with Gaussian states in 1+1 dimensions
We introduce a method to investigate the static and dynamic properties of
both Abelian and non-Abelian lattice gauge models in 1+1 dimensions.
Specifically, we identify a set of transformations that disentangle different
degrees of freedom, and apply a simple Gaussian variational ansatz to the
resulting Hamiltonian. To demonstrate the suitability of the method, we analyze
both static and dynamic aspects of string breaking for the U(1) and SU(2) gauge
models. We benchmark our results against tensor network simulations and observe
excellent agreement, although the number of variational parameters in the
Gaussian ansatz is much smaller.Comment: 19 pages, 6 figures. Added references and corrected typo
Gaussian states for the variational study of (1+1)-dimensional lattice gauge models
We introduce a variational ansatz based on Gaussian states for
(1+1)-dimensional lattice gauge models. To this end we identify a set of
unitary transformations which decouple the gauge degrees of freedom from the
matter fields. Using our ansatz, we study static aspects as well as real-time
dynamics of string breaking in two (1+1)-dimensional theories, namely QED and
two-color QCD. We show that our ansatz captures the relevant features and is in
excellent agreement with data from numerical calculations with tensor networks.Comment: 7 pages, 2 figures, proceedings of the 36th Annual International
Symposium on Lattice Field Theory, 22-28 July, 2018 Michigan State
University, East Lansing, Michigan, US
Simulation of many-qubit quantum computation with matrix product states
Matrix product states provide a natural entanglement basis to represent a
quantum register and operate quantum gates on it. This scheme can be
materialized to simulate a quantum adiabatic algorithm solving hard instances
of a NP-Complete problem. Errors inherent to truncations of the exact action of
interacting gates are controlled by the size of the matrices in the
representation. The property of finding the right solution for an instance and
the expected value of the energy are found to be remarkably robust against
these errors. As a symbolic example, we simulate the algorithm solving a
100-qubit hard instance, that is, finding the correct product state out of ~
10^30 possibilities. Accumulated statistics for up to 60 qubits point at a slow
growth of the average minimum time to solve hard instances with
highly-truncated simulations of adiabatic quantum evolution.Comment: 5 pages, 4 figures, final versio
Matrix Product States for dynamical simulation of infinite chains
We propose a new method for computing the ground state properties and the
time evolution of infinite chains based on a transverse contraction of the
tensor network. The method does not require finite size extrapolation and
avoids explicit truncation of the bond dimension along the evolution. By
folding the network in the time direction prior to contraction, time dependent
expectation values and dynamic correlation functions can be computed after much
longer evolution time than with any previous method. Moreover, the algorithm we
propose can be used for the study of some non-invariant infinite chains,
including impurity models.Comment: 4 pages, 7 EPS figures, extra references and figure; accepted versio
Phase structure of the (1+1)-dimensional massive Thirring model from matrix product states
Employing matrix product states as an ansatz, we study the non-thermal phase
structure of the (1+1)-dimensional massive Thirring model in the sector of
vanishing total fermion number with staggered regularization. In this paper,
details of the implementation for this project are described. To depict the
phase diagram of the model, we examine the entanglement entropy, the fermion
bilinear condensate and two types of correlation functions. Our investigation
shows the existence of two phases, with one of them being critical and the
other gapped. An interesting feature of the phase structure is that the theory
with non-zero fermion mass can be conformal. We also find clear numerical
evidence that these phases are separated by a transition of the
Berezinskii-Kosterlitz-Thouless type. Results presented in this paper establish
the possibility of using the matrix product states for probing this type of
phase transition in quantum field theories. They can provide information for
further exploration of scaling behaviour, and serve as an important ingredient
for controlling the continuum extrapolation of the model.Comment: 31 pages, 18 figures; minor changes to the text, typos corrected,
references added; version published in Physical Review
Quantum walk with a time-dependent coin
We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik [Phys. Rev. Lett. 93, 180601 (2004)] which exhibits interesting dynamical localization and quasiperiodic dynamics. Our proposal allows for a much easier implementation of this particularly rich dynamics than the original one. Moreover, it allows for an additional control on the walk, which can be used to compensate for phases appearing due to external interactions. To illustrate its feasibility, we discuss an example using an optical cavity. We also derive an approximated solution in the continuous limit (long-wavelength approximation) which provides physical insight about the process
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