1,775 research outputs found
The (2+1)-d U(1) Quantum Link Model Masquerading as Deconfined Criticality
The -d U(1) quantum link model is a gauge theory, amenable to quantum
simulation, with a spontaneously broken SO(2) symmetry emerging at a quantum
phase transition. Its low-energy physics is described by a -d \RP(1)
effective field theory, perturbed by a dangerously irrelevant SO(2) breaking
operator, which prevents the interpretation of the emergent pseudo-Goldstone
boson as a dual photon. At the quantum phase transition, the model mimics some
features of deconfined quantum criticality, but remains linearly confining.
Deconfinement only sets in at high temperature.Comment: 4.5 pages, 6 figure
Crystalline Confinement
We show that exotic phases arise in generalized lattice gauge theories known
as quantum link models in which classical gauge fields are replaced by quantum
operators. While these quantum models with discrete variables have a
finite-dimensional Hilbert space per link, the continuous gauge symmetry is
still exact. An efficient cluster algorithm is used to study these exotic
phases. The -d system is confining at zero temperature with a
spontaneously broken translation symmetry. A crystalline phase exhibits
confinement via multi-stranded strings between charge-anti-charge pairs. A
phase transition between two distinct confined phases is weakly first order and
has an emergent spontaneously broken approximate global symmetry. The
low-energy physics is described by a -d effective field
theory, perturbed by a dangerously irrelevant breaking operator, which
prevents the interpretation of the emergent pseudo-Goldstone boson as a dual
photon. This model is an ideal candidate to be implemented in quantum
simulators to study phenomena that are not accessible using Monte Carlo
simulations such as the real-time evolution of the confining string and the
real-time dynamics of the pseudo-Goldstone boson.Comment: Proceedings of the 31st International Symposium on Lattice Field
Theory - LATTICE 201
Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits
A quantum simulator of U(1) lattice gauge theories can be implemented with
superconducting circuits. This allows the investigation of confined and
deconfined phases in quantum link models, and of valence bond solid and spin
liquid phases in quantum dimer models. Fractionalized confining strings and the
real-time dynamics of quantum phase transitions are accessible as well. Here we
show how state-of-the-art superconducting technology allows us to simulate
these phenomena in relatively small circuit lattices. By exploiting the strong
non-linear couplings between quantized excitations emerging when
superconducting qubits are coupled, we show how to engineer gauge invariant
Hamiltonians, including ring-exchange and four-body Ising interactions. We
demonstrate that, despite decoherence and disorder effects, minimal circuit
instances allow us to investigate properties such as the dynamics of electric
flux strings, signaling confinement in gauge invariant field theories. The
experimental realization of these models in larger superconducting circuits
could address open questions beyond current computational capability.Comment: Published versio
SO(3) "Nuclear Physics" with ultracold Gases
An ab initio calculation of nuclear physics from Quantum Chromodynamics
(QCD), the fundamental SU(3) gauge theory of the strong interaction, remains an
outstanding challenge. Here, we discuss the emergence of key elements of
nuclear physics using an SO(3) lattice gauge theory as a toy model for QCD. We
show that this model is accessible to state-of-the-art quantum simulation
experiments with ultracold atoms in an optical lattice. First, we demonstrate
that our model shares characteristic many-body features with QCD, such as the
spontaneous breakdown of chiral symmetry, its restoration at finite baryon
density, as well as the existence of few-body bound states. Then we show that
in the one-dimensional case, the dynamics in the gauge invariant sector can be
encoded as a spin S=3/2 Heisenberg model, i.e., as quantum magnetism, which has
a natural realization with bosonic mixtures in optical lattices, and thus sheds
light on the connection between non-Abelian gauge theories and quantum
magnetism.Comment: 34 pages, 9 figure
Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
Using ultracold alkaline-earth atoms in optical lattices, we construct a
quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic
matter based on quantum link models. These systems share qualitative features
with QCD, including chiral symmetry breaking and restoration at non-zero
temperature or baryon density. Unlike classical simulations, a quantum
simulator does not suffer from sign problems and can address the corresponding
chiral dynamics in real time.Comment: 12 pages, 5 figures. Main text plus one basic introduction to the
topic and one supplementary material on implementation. Final versio
From the Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagom\'e Lattice: Phase Transition and Fractionalized Flux Strings
We consider the -d quantum link model on the honeycomb lattice
and show that it is equivalent to a quantum dimer model on the Kagom\'e
lattice. The model has crystalline confined phases with spontaneously broken
translation invariance associated with pinwheel order, which is investigated
with either a Metropolis or an efficient cluster algorithm. External
half-integer non-Abelian charges (which transform non-trivially under the
center of the gauge group) are confined to each other
by fractionalized strings with a delocalized flux. The strands
of the fractionalized flux strings are domain walls that separate distinct
pinwheel phases. A second-order phase transition in the 3-d Ising universality
class separates two confining phases; one with correlated pinwheel
orientations, and the other with uncorrelated pinwheel orientations.Comment: 16 pages, 20 figures, 2 tables, two more relevant references and one
short paragraph are adde
From the Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagom\'e Lattice: Phase Transition and Fractionalized Flux Strings
We consider the -d quantum link model on the honeycomb lattice
and show that it is equivalent to a quantum dimer model on the Kagom\'e
lattice. The model has crystalline confined phases with spontaneously broken
translation invariance associated with pinwheel order, which is investigated
with either a Metropolis or an efficient cluster algorithm. External
half-integer non-Abelian charges (which transform non-trivially under the
center of the gauge group) are confined to each other
by fractionalized strings with a delocalized flux. The strands
of the fractionalized flux strings are domain walls that separate distinct
pinwheel phases. A second-order phase transition in the 3-d Ising universality
class separates two confining phases; one with correlated pinwheel
orientations, and the other with uncorrelated pinwheel orientations.Comment: 16 pages, 20 figures, 2 tables, two more relevant references and one
short paragraph are adde
Finite-Volume Energy Spectrum, Fractionalized Strings, and Low-Energy Effective Field Theory for the Quantum Dimer Model on the Square Lattice
We present detailed analytic calculations of finite-volume energy spectra,
mean field theory, as well as a systematic low-energy effective field theory
for the square lattice quantum dimer model. The analytic considerations explain
why a string connecting two external static charges in the confining columnar
phase fractionalizes into eight distinct strands with electric flux
. An emergent approximate spontaneously broken symmetry
gives rise to a pseudo-Goldstone boson. Remarkably, this soft phonon-like
excitation, which is massless at the Rokhsar-Kivelson (RK) point, exists far
beyond this point. The Goldstone physics is captured by a systematic low-energy
effective field theory. We determine its low-energy parameters by matching the
analytic effective field theory with exact diagonalization results and Monte
Carlo data. This confirms that the model exists in the columnar (and not in a
plaquette or mixed) phase all the way to the RK point.Comment: 35 pages, 16 figure
Microscopic Model versus Systematic Low-Energy Effective Field Theory for a Doped Quantum Ferromagnet
We consider a microscopic model for a doped quantum ferromagnet as a test
case for the systematic low-energy effective field theory for magnons and
holes, which is constructed in complete analogy to the case of quantum
antiferromagnets. In contrast to antiferromagnets, for which the effective
field theory approach can be tested only numerically, in the ferromagnetic case
both the microscopic and the effective theory can be solved analytically. In
this way the low-energy parameters of the effective theory are determined
exactly by matching to the underlying microscopic model. The low-energy
behavior at half-filling as well as in the single- and two-hole sectors is
described exactly by the systematic low-energy effective field theory. In
particular, for weakly bound two-hole states the effective field theory even
works beyond perturbation theory. This lends strong support to the quantitative
success of the systematic low-energy effective field theory method not only in
the ferromagnetic but also in the physically most interesting antiferromagnetic
case.Comment: 34 pages, 1 figur
Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension
The functional RG for the random field and random anisotropy O(N)
sigma-models is studied to two loop. The ferromagnetic/disordered (F/D)
transition fixed point is found to next order in d=4+epsilon for N > N_c
(N_c=2.8347408 for random field, N_c=9.44121 for random anisotropy). For N <
N_c the lower critical dimension plunges below d=4: we find two fixed points,
one describing the quasi-ordered phase, the other is novel and describes the
F/D transition. The lower critical dimension can be obtained in an
(N_c-N)-expansion. The theory is also analyzed at large N and a glassy regime
is found.Comment: 4 pages, 5 figure
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