83 research outputs found
Towards Quantum Simulating QCD
Quantum link models provide an alternative non-perturbative formulation of
Abelian and non-Abelian lattice gauge theories. They are ideally suited for
quantum simulation, for example, using ultracold atoms in an optical lattice.
This holds the promise to address currently unsolvable problems, such as the
real-time and high-density dynamics of strongly interacting matter, first in
toy-model gauge theories, and ultimately in QCD.Comment: 8 pages, 4 figures, plenary talk at Quark Matter 2014, submitted as a
proceedings contribution to Nuclear Physics
Non-trivial \theta-Vacuum Effects in the 2-d O(3) Model
We study \theta-vacua in the 2-d lattice O(3) model using the standard action
and an optimized constraint action with very small cut-off effects, combined
with the geometric topological charge. Remarkably, dislocation lattice
artifacts do not spoil the non-trivial continuum limit at \theta\ non-zero, and
there are different continuum theories for each value of \theta. A very precise
Monte Carlo study of the step scaling function indirectly confirms the exact
S-matrix of the 2-d O(3) model at \theta = \pi.Comment: 4 pages, 3 figure
Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
Quantum Monte Carlo simulations, while being efficient for bosons, suffer
from the "negative sign problem'' when applied to fermions - causing an
exponential increase of the computing time with the number of particles. A
polynomial time solution to the sign problem is highly desired since it would
provide an unbiased and numerically exact method to simulate correlated quantum
systems. Here we show, that such a solution is almost certainly unattainable by
proving that the sign problem is NP-hard, implying that a generic solution of
the sign problem would also solve all problems in the complexity class NP
(nondeterministic polynomial) in polynomial time.Comment: 4 page
Real-Time Evolution of Strongly Coupled Fermions driven by Dissipation
We consider the real-time evolution of a strongly coupled system of lattice
fermions whose dynamics is driven entirely by dissipative Lindblad processes,
with linear or quadratic quantum jump operators. The fermion 2-point functions
obey a closed set of differential equations, which can be solved with linear
algebra methods. The staggered occupation order parameter of the t-V model
decreases exponentially during the dissipative time evolution. The structure
factor associated with the various Fourier modes shows the slowing down of
low-momentum modes, which is due to particle number conservation. The processes
with nearest-neighbor-dependent Lindblad operators have a decay rate that is
proportional to the coordination number of the spatial lattice.Comment: 15 pages, 4 figure
Dissipative Bose-Einstein condensation in contact with a thermal reservoir
We investigate the real-time dynamics of open quantum spin- or hardcore
boson systems on a spatial lattice, which are governed by a Markovian quantum
master equation. We derive general conditions under which the hierarchy of
correlation functions closes such that their time evolution can be computed
semi-analytically. Expanding our previous work [Phys. Rev. A 93, 021602 (2016)]
we demonstrate the universality of a purely dissipative quantum Markov process
that drives the system of spin- particles into a totally symmetric
superposition state, corresponding to a Bose-Einstein condensate of hardcore
bosons. In particular, we show that the finite-size scaling behavior of the
dissipative gap is independent of the chosen boundary conditions and the
underlying lattice structure. In addition, we consider the effect of a uniform
magnetic field as well as a coupling to a thermal bath to investigate the
susceptibility of the engineered dissipative process to unitary and nonunitary
perturbations. We establish the nonequilibrium steady-state phase diagram as a
function of temperature and dissipative coupling strength. For a small number
of particles , we identify a parameter region in which the engineered
symmetrizing dissipative process performs robustly, while in the thermodynamic
limit , the coupling to the thermal bath destroys any
long-range order.Comment: 30 pages, 8 figures; Revised version: Minor changes and references
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