235 research outputs found
Equilibration in low-dimensional quantum matrix models
Matrix models play an important role in studies of quantum gravity, being
candidates for a formulation of M-theory, but are notoriously difficult to
solve. In this work, we present a fresh approach by introducing a novel exact
model provably equivalent with low-dimensional bosonic matrix models. In this
equivalent model significant local structure becomes apparent and it can serve
as a simple toy model for analytical and precise numerical study. We derive a
substantial part of the low energy spectrum, find a conserved charge, and are
able to derive numerically the Regge trajectories. To exemplify the usefulness
of the approach, we address questions of equilibration starting from a
non-equilibrium situation, building upon an intuition from quantum information.
We finally discuss possible generalizations of the approach.Comment: 5+2 pages, 2 figures; v2: published versio
Continuous matrix product state tomography of quantum transport experiments
In recent years, a close connection between the description of open quantum
systems, the input-output formalism of quantum optics, and continuous matrix
product states in quantum field theory has been established. So far, however,
this connection has not been extended to the condensed-matter context. In this
work, we substantially develop further and apply a machinery of continuous
matrix product states (cMPS) to perform tomography of transport experiments. We
first present an extension of the tomographic possibilities of cMPS by showing
that reconstruction schemes do not need to be based on low-order correlation
functions only, but also on low-order counting probabilities. We show that
fermionic quantum transport settings can be formulated within the cMPS
framework. This allows us to present a reconstruction scheme based on the
measurement of low-order correlation functions that provides access to
quantities that are not directly measurable with present technology. Emblematic
examples are high-order correlations functions and waiting times distributions
(WTD). The latter are of particular interest since they offer insights into
short-time scale physics. We demonstrate the functioning of the method with
actual data, opening up the way to accessing WTD within the quantum regime.Comment: 11 pages, 4 figure
Quantum field tomography
We introduce the concept of quantum field tomography, the efficient and
reliable reconstruction of unknown quantum fields based on data of correlation
functions. At the basis of the analysis is the concept of continuous matrix
product states, a complete set of variational states grasping states in quantum
field theory. We innovate a practical method, making use of and developing
tools in estimation theory used in the context of compressed sensing such as
Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum
field states based on low-order correlation functions. In the absence of a
phase reference, we highlight how specific higher order correlation functions
can still be predicted. We exemplify the functioning of the approach by
reconstructing randomised continuous matrix product states from their
correlation data and study the robustness of the reconstruction for different
noise models. We also apply the method to data generated by simulations based
on continuous matrix product states and using the time-dependent variational
principle. The presented approach is expected to open up a new window into
experimentally studying continuous quantum systems, such as encountered in
experiments with ultra-cold atoms on top of atom chips. By virtue of the
analogy with the input-output formalism in quantum optics, it also allows for
studying open quantum systems.Comment: 31 pages, 5 figures, minor change
Classical spin systems and the quantum stabilizer formalism: general mappings and applications
We present general mappings between classical spin systems and quantum
physics. More precisely, we show how to express partition functions and
correlation functions of arbitrary classical spin models as inner products
between quantum stabilizer states and product states, thereby generalizing
mappings for some specific models established in [Phys. Rev. Lett. 98, 117207
(2007)]. For Ising- and Potts-type models with and without external magnetic
field, we show how the entanglement features of the corresponding stabilizer
states are related to the interaction pattern of the classical model, while the
choice of product states encodes the details of interaction. These mappings
establish a link between the fields of classical statistical mechanics and
quantum information theory, which we utilize to transfer techniques and methods
developed in one field to gain insight into the other. For example, we use
quantum information techniques to recover well known duality relations and
local symmetries of classical models in a simple way, and provide new classical
simulation methods to simulate certain types of classical spin models. We show
that in this way all inhomogeneous models of q-dimensional spins with pairwise
interaction pattern specified by a graph of bounded tree-width can be simulated
efficiently. Finally, we show relations between classical spin models and
measurement-based quantum computation.Comment: 24 pages, 5 figures, minor corrections, version as accepted in JM
Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent systems
Traditionally, superconductors are categorized as type-I or type-II. Type-I
superconductors support only Meissner and normal states, while type-II
superconductors form magnetic vortices in sufficiently strong applied magnetic
fields. Recently there has been much interest in superconducting systems with
several species of condensates, in fields ranging from Condensed Matter to High
Energy Physics. Here we show that the type-I/type-II classification is
insufficient for such multicomponent superconductors. We obtain solutions
representing thermodynamically stable vortices with properties falling outside
the usual type-I/type-II dichotomy, in that they have the following features:
(i) Pippard electrodynamics, (ii) interaction potential with long-range
attractive and short-range repulsive parts, (iii) for an n-quantum vortex, a
non-monotonic ratio E(n)/n where E(n) is the energy per unit length, (iv)
energetic preference for non-axisymmetric vortex states, "vortex molecules".
Consequently, these superconductors exhibit an emerging first order transition
into a "semi-Meissner" state, an inhomogeneous state comprising a mixture of
domains of two-component Meissner state and vortex clusters.Comment: in print in Phys. Rev. B Rapid Communications. v2: presentation is
made more accessible for a general reader. Latest updates and links to
related papers are available at the home page of one of the authors:
http://people.ccmr.cornell.edu/~egor
Renormalization algorithm with graph enhancement
We introduce a class of variational states to describe quantum many-body
systems. This class generalizes matrix product states which underly the
density-matrix renormalization group approach by combining them with weighted
graph states. States within this class may (i) possess arbitrarily long-ranged
two-point correlations, (ii) exhibit an arbitrary degree of block entanglement
entropy up to a volume law, (iii) may be taken translationally invariant, while
at the same time (iv) local properties and two-point correlations can be
computed efficiently. This new variational class of states can be thought of as
being prepared from matrix product states, followed by commuting unitaries on
arbitrary constituents, hence truly generalizing both matrix product and
weighted graph states. We use this class of states to formulate a
renormalization algorithm with graph enhancement (RAGE) and present numerical
examples demonstrating that improvements over density-matrix renormalization
group simulations can be achieved in the simulation of ground states and
quantum algorithms. Further generalizations, e.g., to higher spatial
dimensions, are outlined.Comment: 4 pages, 1 figur
Solving condensed-matter ground-state problems by semidefinite relaxations
We present a new generic approach to the condensed-matter ground-state
problem which is complementary to variational techniques and works directly in
the thermodynamic limit. Relaxing the ground-state problem, we obtain
semidefinite programs (SDP). These can be solved efficiently, yielding strict
lower bounds to the ground-state energy and approximations to the few-particle
Green's functions. As the method is applicable for all particle statistics, it
represents in particular a novel route for the study of strongly correlated
fermionic and frustrated spin systems in D>1 spatial dimensions. It is
demonstrated for the XXZ model and the Hubbard model of spinless fermions. The
results are compared against exact solutions, quantum Monte Carlo, and Anderson
bounds, showing the competitiveness of the SDP method.Comment: 8 pages, 3 figures; original title "Approaching condensed matter
ground states from below"; improved numerics, added references; published
version, including appendice
Wick's theorem for matrix product states
Matrix-product states and their continuous analogues are variational classes
of states that capture quantum many-body systems or quantum fields with low
entanglement; they are at the basis of the density-matrix renormalization group
method and continuous variants thereof. In this work we show that, generically,
N-point functions of arbitrary operators in discrete and continuous
translationally invariant matrix product states are completely characterized by
the corresponding two- and three-point functions. Aside from having important
consequences for the structure of correlations in quantum states with low
entanglement, this result provides a new way of reconstructing unknown states
from correlation measurements, e.g., for one-dimensional continuous systems of
cold atoms. We argue that such a relation of correlation functions may help in
devising perturbative approaches to interacting theories.Comment: 6 pages, final versio
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