12 research outputs found
Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
We investigate the finite-density phase diagram of a non-abelian SU(2)
lattice gauge theory in (1+1)-dimensions using tensor network methods. We
numerically characterise the phase diagram as a function of the matter filling
and of the matter-field coupling, identifying different phases, some of them
appearing only at finite densities. For weak matter-field coupling we find a
meson BCS liquid phase, which is confirmed by second-order analytical
perturbation theory. At unit filling and for strong coupling, the system
undergoes a phase transition to a charge density wave of single-site (spin-0)
mesons via spontaneous chiral symmetry breaking. At finite densities, the
chiral symmetry is restored almost everywhere, and the meson BCS liquid becomes
a simple liquid at strong couplings, with the exception of filling two-thirds,
where a charge density wave of mesons spreading over neighbouring sites
appears. Finally, we identify two tri-critical points between the chiral and
the two liquid phases which are compatible with a
Wess-Zumino-Novikov-Witten model. Here we do not perform the continuum limit
but we explicitly address the global charge conservation symmetry.Comment: 13 pages, 8 figure
Phase Diagram and Conformal String Excitations of Square Ice using Gauge Invariant Matrix Product States
We investigate the ground state phase diagram of square ice -- a U(1) lattice
gauge theory in two spatial dimensions -- using gauge invariant tensor network
techniques. By correlation function, Wilson loop, and entanglement diagnostics,
we characterize its phases and the transitions between them, finding good
agreement with previous studies. We study the entanglement properties of string
excitations on top of the ground state, and provide direct evidence of the fact
that the latter are described by a conformal field theory. Our results pave the
way to the application of tensor network methods to confining, two-dimensional
lattice gauge theories, to investigate their phase diagrams and low-lying
excitations.Comment: 36 pages, 16 figures; referee suggestions incorporated, added Figs.
3, 13 and appendices A,
Superfluid density and quasi-long-range order in the one-dimensional disordered Bose-Hubbard model
We study the equilibrium properties of the one-dimensional disordered
Bose-Hubbard model by means of a gauge-adaptive tree tensor network variational
method suitable for systems with periodic boundary conditions. We compute the
superfluid stiffness and superfluid correlations close to the superfluid to
glass transition line, obtaining accurate locations of the critical points. By
studying the statistics of the exponent of the power-law decay of the
correlation, we determine the boundary between the superfluid region and the
Bose glass phase in the regime of strong disorder and in the weakly interacting
region, not explored numerically before. In the former case our simulations are
in agreement with previous Monte Carlo calculations.Comment: 18 pages, 12 figures; some references and two appendices added;
appearing in New Journal of Physics focus issue "Strongly Interacting Quantum
Gases in One Dimension
Density-of-states of many-body quantum systems from tensor networks
We present a technique to compute the microcanonical thermodynamical
properties of a manybody quantum system using tensor networks. The Density Of
States (DOS), and more general spectral properties, are evaluated by means of a
Hubbard-Stratonovich transformation performed on top of a real-time evolution,
which is carried out via numerical methods based on tensor networks. As a
consequence, the free energy and thermal averages can be also calculated. We
test this approach on the one-dimensional Ising and Fermi-Hubbard models. Using
matrix product states, we show that the thermodynamical quantities as a
function of temperature are in very good agreement with the exact results. This
approach can be extended to higher-dimensional system by properly employing
other types of tensor networks.Comment: 8 pages, 7 figure
The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
We present a compendium of numerical simulation techniques, based on tensor
network methods, aiming to address problems of many-body quantum mechanics on a
classical computer. The core setting of this anthology are lattice problems in
low spatial dimension at finite size, a physical scenario where tensor network
methods, both Density Matrix Renormalization Group and beyond, have long proven
to be winning strategies. Here we explore in detail the numerical frameworks
and methods employed to deal with low-dimension physical setups, from a
computational physics perspective. We focus on symmetries and closed-system
simulations in arbitrary boundary conditions, while discussing the numerical
data structures and linear algebra manipulation routines involved, which form
the core libraries of any tensor network code. At a higher level, we put the
spotlight on loop-free network geometries, discussing their advantages, and
presenting in detail algorithms to simulate low-energy equilibrium states.
Accompanied by discussions of data structures, numerical techniques and
performance, this anthology serves as a programmer's companion, as well as a
self-contained introduction and review of the basic and selected advanced
concepts in tensor networks, including examples of their applications.Comment: 115 pages, 56 figure
Tensor Network Simulation of compact one-dimensional lattice Quantum Chromodynamics at finite density
We perform a zero temperature analysis of a non-Abelian lattice gauge model
corresponding to an SU(3) Yang Mills theory in 1+1D at low energies.
Specifically, we characterize the model ground states via gauge-invariant
Matrix Product States, identifying its phase diagram at finite density as a
function of the matter-gauge interaction coupling, the quark filling, and their
bare mass. Overall, we observe an extreme robustness of baryons: For positive
free-field energy couplings, all detected phases exhibit colorless
quasiparticles, a strong numerical hint that QCD does not deconfine in 1D.
Additionally, we show that having access to finite-density properties, it is
possible to study the stability of composite particles, including multi-baryon
bound states, such as the deuteron.Comment: 9 pages, 5 figure
Dynamical Ginzburg criterion for the quantum-classical crossover of the Kibble-Zurek mechanism
We introduce a simple criterion for lattice models to predict quantitatively
the crossover between the classical and the quantum scaling of the Kibble-Zurek
mechanism, as the one observed in a quantum -model on a 1D lattice
[Phys. Rev. Lett. 116, 225701 (2016)]. We corroborate that the crossover is a
general feature of critical models on a lattice, by testing our paradigm on the
quantum Ising model in transverse field for arbitrary spin- ()
in one spatial dimension. By means of tensor network methods, we fully
characterize the equilibrium properties of this model, and locate the quantum
critical regions via our dynamical Ginzburg criterion. We numerically simulate
the Kibble-Zurek quench dynamics and show the validity of our picture, also
according to finite-time scaling analysis.Comment: 12 pages, 13 figure
Phase diagram and conformal string excitations of square ice using gauge invariant matrix product states
We investigate the ground state phase diagram of square ice -- a U(1) lattice
gauge theory in two spatial dimensions -- using gauge invariant tensor network
techniques. By correlation function, Wilson loop, and entanglement diagnostics,
we characterize its phases and the transitions between them, finding good
agreement with previous studies. We study the entanglement properties of string
excitations on top of the ground state, and provide direct evidence of the fact
that the latter are described by a conformal field theory. Our results pave the
way to the application of tensor network methods to confining, two-dimensional
lattice gauge theories, to investigate their phase diagrams and low-lying
excitations
Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states
We provide evidence that randomized low-rank factorization is a powerful tool for the determination of the ground-state properties of low-dimensional lattice Hamiltonians through tensor network techniques. In particular, we show that randomized matrix factorization outperforms truncated singular value decomposition based on state-of-the-art deterministic routines in time-evolving block decimation (TEBD)- and density matrix renormalization group (DMRG)-style simulations, even when the system under study gets close to a phase transition: We report linear speedups in the bond or local dimension of up to 24 times in quasi-two-dimensional cylindrical systems