66 research outputs found
Fermionic Projected Entangled Pair States at Finite Temperature
An algorithm for imaginary time evolution of a fermionic projected entangled
pair state (PEPS) with ancillas from infinite temperature down to a finite
temperature state is presented. As a benchmark application, it is applied to
spinless fermions hopping on a square lattice subject to -wave pairing
interactions. With a tiny bias it allows to evolve the system across a
high-temperature continuous symmetry-breaking phase transition.Comment: 7 pages, 11 figures; new results on a high-Tc phase transition were
adde
Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles
A typical quantum state obeying the area law for entanglement on an infinite
2D lattice can be represented by a tensor network ansatz -- known as an
infinite projected entangled pair state (iPEPS) -- with a finite bond dimension
. Its real/imaginary time evolution can be split into small time steps. An
application of a time step generates a new iPEPS with a bond dimension
times the original one. The new iPEPS does not make optimal use of its enlarged
bond dimension , hence in principle it can be represented accurately by a
more compact ansatz, favourably with the original . In this work we show how
the more compact iPEPS can be optimized variationally to maximize its overlap
with the new iPEPS. To compute the overlap we use the corner transfer matrix
renormalization group (CTMRG). By simulating sudden quench of the transverse
field in the 2D quantum Ising model with the proposed algorithm, we provide a
proof of principle that real time evolution can be simulated with iPEPS. A
similar proof is provided in the same model for imaginary time evolution of
purification of its thermal states.Comment: 9 pages, 10 figures, replaced with the published versio
Variational Approach to Projected Entangled Pair States at Finite Temperature
The projected entangled pair state (PEPS) ansatz can represent a thermal
state in a strongly correlated system. We introduce a novel variational
algorithm to optimize this tensor network. Since full tensor environment is
taken into account, then with increasing bond dimension the optimized PEPS
becomes the exact Gibbs state. Our presentation opens with a 1D version for a
matrix product state (MPS) and then generalizes to PEPS in 2D. Benchmark
results in the quantum Ising model are presented.Comment: 9 pages, 12 figures; an extended version with new numerical result
Projected Entangled Pair States at Finite Temperature: Iterative Self-Consistent Bond Renormalization for Exact Imaginary Time Evolution
A projected entangled pair state (PEPS) with ancillas can be evolved in
imaginary time to obtain thermal states of a strongly correlated quantum system
on a 2D lattice. Every application of a Suzuki-Trotter gate multiplies the PEPS
bond dimension by a factor . It has to be renormalized back to the
original . In order to preserve the accuracy of the Suzuki-Trotter (S-T)
decomposition, the renormalization has in principle to take into account full
environment made of the new tensors with the bond dimension . Here
we propose a self-consistent renormalization procedure operating with the
original bond dimension , but without compromising the accuracy of the S-T
decomposition. The iterative procedure renormalizes the bond using full
environment made of renormalized tensors with the bond dimension . After
every renormalization, the new renormalized tensors are used to update the
environment, and then the renormalization is repeated again and again until
convergence. As a benchmark application, we obtain thermal states of the
transverse field quantum Ising model on a square lattice - both infinite and
finite - evolving the system across a second-order phase transition at finite
temperature.Comment: 9 pages, 14 figures, improved presentation. arXiv admin note: text
overlap with arXiv:1311.727
Striped critical spin liquid in a spin-orbital entangled RVB state in a projected entangled-pair state representation
We introduce a spin-orbital entangled (SOE) resonating valence bond (RVB)
state on a square lattice of spins- and orbitals represented by
pseudospins-. Like the standard RVB state, it is a superposition of
nearest-neighbor hard-core coverings of the lattice by spin singlets, but
adjacent singlets are favoured to have perpendicular orientations and, more
importantly, an orientation of each singlet is entangled with orbitals' state
on its two lattice sites. The SOE-RVB state can be represented by a projected
entangled pair state (PEPS) with a bond dimension . This representation
helps to reveal that the state is a superposition of striped coverings
conserving a topological quantum number. The stripes are a critical quantum
spin liquid. We propose a spin-orbital Hamiltonian supporting a SOE-RVB ground
state.Comment: 8 pages, 10 figure
Projected Entangled Pair States at Finite Temperature: Imaginary Time Evolution with Ancillas
A projected entangled pair state (PEPS) with ancillas is evolved in imaginary
time. This tensor network represents a thermal state of a 2D lattice quantum
system. A finite temperature phase diagram of the 2D quantum Ising model in a
transverse field is obtained as a benchmark application.Comment: 7 pages, 9 figures; version accepted to publication in Phys. Rev. B;
added new numerical results and reference
Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
An infinite projected entangled pair state (iPEPS) is a tensor network ansatz
to represent a quantum state on an infinite 2D lattice whose accuracy is
controlled by the bond dimension . Its real, Lindbladian or imaginary time
evolution can be split into small time steps. Every time step generates a new
iPEPS with an enlarged bond dimension , which is approximated by an
iPEPS with the original . In Phys. Rev. B 98, 045110 (2018) an algorithm was
introduced to optimize the approximate iPEPS by maximizing directly its
fidelity to the one with the enlarged bond dimension . In this work we
implement a more efficient optimization employing a local estimator of the
fidelity. For imaginary time evolution of a thermal state's purification, we
also consider using unitary disentangling gates acting on ancillas to reduce
the required . We test the algorithm simulating Lindbladian evolution and
unitary evolution after a sudden quench of transverse field in the 2D
quantum Ising model. Furthermore, we simulate thermal states of this model and
estimate the critical temperature with good accuracy: for and
for the more challenging case of close to the quantum
critical point at .Comment: published version, presentation improve
Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital Model on an Infinite Square Lattice
The variational tensor network renormalization approach to two-dimensional
(2D) quantum systems at finite temperature is applied for the first time to a
model suffering the notorious quantum Monte Carlo sign problem --- the orbital
model with spatially highly anisotropic orbital interactions.
Coarse-graining of the tensor network along the inverse temperature
yields a numerically tractable 2D tensor network representing the Gibbs state.
Its bond dimension --- limiting the amount of entanglement --- is a natural
refinement parameter. Increasing we obtain a converged order parameter and
its linear susceptibility close to the critical point. They confirm the
existence of finite order parameter below the critical temperature ,
provide a numerically exact estimate of~, and give the critical exponents
within of the 2D Ising universality class.Comment: 8 pages, 8 figure
Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature
Progress in describing thermodynamic phase transitions in quantum systems is
obtained by noticing that the Gibbs operator for a
two-dimensional (2D) lattice system with a Hamiltonian can be represented
by a three-dimensional tensor network, the third dimension being the imaginary
time (inverse temperature) . Coarse-graining the network along
results in a 2D projected entangled-pair operator (PEPO) with a finite bond
dimension . The coarse-graining is performed by a tree tensor network of
isometries. The isometries are optimized variationally --- taking into account
full tensor environment --- to maximize the accuracy of the PEPO. The algorithm
is applied to the isotropic quantum compass model on an infinite square lattice
near a symmetry-breaking phase transition at finite temperature. From the
linear susceptibility in the symmetric phase and the order parameter in the
symmetry-broken phase the critical temperature is estimated at , where is the isotropic coupling constant between
pseudospins.Comment: 12 pages, 15 figures, slightly revised after referees' report
Order in quantum compass and orbital e_{g} models
We investigate thermodynamic phase transitions in the compass model and in
orbital model on an infinite square lattice by variational tensor network
renormalization (VTNR) in imaginary time. The onset of nematic order in the
quantum compass model is estimated at . For~the
orbital model one finds: () a very accurate estimate of and ()~the~critical exponents in the Ising
universality class. Remarkably large difference in frustration results in so
distinct values of , while entanglement influences the quality of
estimation.Comment: 4 pages, 2 figures, accepted by Acta Physica Polonica
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