84 research outputs found
Entanglement entropy of two disjoint blocks in critical Ising models
We study the scaling of the Renyi and entanglement entropy of two disjoint
blocks of critical Ising models, as function of their sizes and separations. We
present analytic results based on conformal field theory that are
quantitatively checked in numerical simulations of both the quantum spin chain
and the classical two dimensional Ising model. Theoretical results match the
ones obtained from numerical simulations only after taking properly into
account the corrections induced by the finite length of the blocks to their
leading scaling behavior.Comment: 4 pages, 5 figures. Revised version accepted for publication in PR
Tensor Networks for Lattice Gauge Theories with continuous groups
We discuss how to formulate lattice gauge theories in the Tensor Network
language. In this way we obtain both a consistent truncation scheme of the
Kogut-Susskind lattice gauge theories and a Tensor Network variational ansatz
for gauge invariant states that can be used in actual numerical computation.
Our construction is also applied to the simplest realization of the quantum
link models/gauge magnets and provides a clear way to understand their
microscopic relation with Kogut-Susskind lattice gauge theories. We also
introduce a new set of gauge invariant operators that modify continuously
Rokshar-Kivelson wave functions and can be used to extend the phase diagram of
known models. As an example we characterize the transition between the
deconfined phase of the lattice gauge theory and the Rokshar-Kivelson
point of the U(1) gauge magnet in 2D in terms of entanglement entropy. The
topological entropy serves as an order parameter for the transition but not the
Schmidt gap.Comment: 27 pages, 25 figures, 2nd version the same as the published versio
Toolbox for Abelian lattice gauge theories with synthetic matter
Fundamental forces of Nature are described by field theories, also known as
gauge theories, based on a local gauge invariance. The simplest of them is
quantum electrodynamics (QED), which is an example of an Abelian gauge theory.
Such theories describe the dynamics of massless photons and their coupling to
matter. However, in two spatial dimension (2D) they are known to exhibit gapped
phases at low temperature. In the realm of quantum spin systems, it remains a
subject of considerable debate if their low energy physics can be described by
emergent gauge degrees of freedom. Here we present a class of simple
two-dimensional models that admit a low energy description in terms of an
Abelian gauge theory. We find rich phase diagrams for these models comprising
exotic deconfined phases and gapless phases - a rare example for 2D Abelian
gauge theories. The counter-intuitive presence of gapless phases in 2D results
from the emergence of additional symmetry in the models. Moreover, we propose
schemes to realize our model with current experiments using ultracold bosonic
atoms in optical lattices.Comment: Accepted versio
Characterizing the quantum field theory vacuum using temporal Matrix Product states
In this paper we construct the continuous Matrix Product State (MPS)
representation of the vacuum of the field theory corresponding to the
continuous limit of an Ising model. We do this by exploiting the observation
made by Hastings and Mahajan in [Phys. Rev. A \textbf{91}, 032306 (2015)] that
the Euclidean time evolution generates a continuous MPS along the time
direction. We exploit this fact, together with the emerging Lorentz invariance
at the critical point in order to identify the matrix product representation of
the quantum field theory (QFT) vacuum with the continuous MPS in the time
direction (tMPS). We explicitly construct the tMPS and check these statements
by comparing the physical properties of the tMPS with those of the standard
ground MPS. We furthermore identify the QFT that the tMPS encodes with the
field theory emerging from taking the continuous limit of a weakly perturbed
Ising model by a parallel field first analyzed by Zamolodchikov.Comment: The results presented in this paper are a significant expansion of
arXiv:1608.0654
Entanglement entropy for the long range Ising chain
We consider the Ising model in a transverse field with long-range
antiferromagnetic interactions that decay as a power law with their distance.
We study both the phase diagram and the entanglement properties as a function
of the exponent of the interaction. The phase diagram can be used as a guide
for future experiments with trapped ions. We find two gapped phases, one
dominated by the transverse field, exhibiting quasi long range order, and one
dominated by the long range interaction, with long range N\'eel ordered ground
states. We determine the location of the quantum critical points separating
those two phases. We determine their critical exponents and central-charges. In
the phase with quasi long range order the ground states exhibit exotic
corrections to the area law for the entanglement entropy coexisting with gapped
entanglement spectra.Comment: 5 pages, all comments welcom
Direct numerical computation of disorder parameters
In the framework of various statistical models as well as of mechanisms for
color confinement, disorder parameters can be developed which are generally
expressed as ratios of partition functions and whose numerical determination is
usually challenging. We develop an efficient method for their computation and
apply it to the study of dual superconductivity in 4d compact U(1) gauge
theory.Comment: 5 pages, 6 figures. Final revised version published in PR
Locality of temperature in spin chains
In traditional thermodynamics, temperature is a local quantity: a subsystem
of a large thermal system is in a thermal state at the same temperature as the
original system. For strongly interacting systems, however, the locality of
temperature breaks down. We study the possibility of associating an effective
thermal state to subsystems of infinite chains of interacting spin particles of
arbitrary finite dimension. We study the effect of correlations and criticality
in the definition of this effective thermal state and discuss the possible
implications for the classical simulation of thermal quantum systems.Comment: 18+9 pages, 12 figure
On temporal entropy and the complexity of computing the expectation value of local operators after a quench
We study the computational complexity of simulating the time-dependent
expectation value of a local operator in a one-dimensional quantum system by
using temporal matrix product states. We argue that such cost is intimately
related to that of encoding temporal transition matrices and their partial
traces. In particular, we show that we can upper-bound the rank of these
reduced transition matrices by the one of the Heisenberg evolution of local
operators, thus making connection between two apparently different quantities,
the temporal entanglement and the local operator entanglement. As a result,
whenever the local operator entanglement grows slower than linearly in time, we
show that computing time-dependent expectation values of local operators using
temporal matrix product states is likely advantageous with respect to computing
the same quantities using standard matrix product states techniques.Comment: 6+3 pages, 8 figure
Converting long-range entanglement into mixture: tensor-network approach to local equilibration
In the out-of-equilibrium evolution induced by a quench, fast degrees of
freedom generate long-range entanglement that is hard to encode with standard
tensor networks. However, local observables only sense such long-range
correlations through their contribution to the reduced local state as a
mixture. We present a tensor network method that identifies such long-range
entanglement and efficiently transforms it into mixture, much easier to
represent. In this way, we obtain an effective description of the time-evolved
state as a density matrix that captures the long-time behavior of local
operators with finite computational resources.Comment: 5 pages, 4 figures, comments are welcome
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