579 research outputs found
Improved energy extrapolation with infinite projected entangled-pair states applied to the 2D Hubbard model
An infinite projected entangled-pair state (iPEPS) is a variational tensor
network ansatz for 2D wave functions in the thermodynamic limit where the
accuracy can be systematically controlled by the bond dimension . We show
that for the doped Hubbard model in the strongly correlated regime (,
) iPEPS yields lower variational energies than state-of-the-art
variational methods in the large 2D limit, which demonstrates the
competitiveness of the method. In order to obtain an accurate estimate of the
energy in the exact infinite limit we introduce and test an extrapolation
technique based on a truncation error computed in the iPEPS imaginary time
evolution algorithm. The extrapolated energies are compared with accurate
quantum Monte Carlo results at half filling and with various other methods in
the doped, strongly correlated regime.Comment: 8 pages, 6 figure
Variational optimization with infinite projected entangled-pair states
We present a scheme to perform an iterative variational optimization with
infinite projected entangled-pair states (iPEPS), a tensor network ansatz for a
two-dimensional wave function in the thermodynamic limit, to compute the ground
state of a local Hamiltonian. The method is based on a systematic summation of
Hamiltonian contributions using the corner transfer-matrix method. Benchmark
results for challenging problems are presented, including the 2D Heisenberg
model, the Shastry-Sutherland model, and the t-J model, which show that the
variational scheme yields considerably more accurate results than the
previously best imaginary time evolution algorithm, with a similar
computational cost and with a faster convergence towards the ground state.Comment: 11 pages, 9 figures, revised (published) version, correction in Fig.
Emergent Haldane phase in the bilinear-biquadratic Heisenberg model on the square lattice
Infinite projected entangled pair states simulations of the
bilinear-biquadratic Heisenberg model on the square lattice reveal an emergent
Haldane phase in between the previously predicted antiferromagnetic and
3-sublattice 120 magnetically ordered phases. This intermediate phase
preserves SU(2) spin and translational symmetry but breaks lattice rotational
symmetry, and it can be adiabatically connected to the Haldane phase of
decoupled chains. Our results contradict previous studies which found a
direct transition between the two magnetically ordered states.Comment: 5 pages, 4 figures, plus supplemental materia
A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice
Using infinite projected entangled pair states, we study the ground state
phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square
lattice directly in the thermodynamic limit. We find an unexpected partially
nematic partially magnetic phase in between the antiferroquadrupolar and
ferromagnetic regions. Furthermore, we describe all observed phases and discuss
the nature of the phase transitions involved.Comment: 27 pages, 15 figures; v3: adjusted sections 1 and 3, and added a
paragraph to section 5.2.
A ground state study of the spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice using tensor networks
Making use of infinite projected entangled pair states, we investigate the
ground state phase diagram of the nearest-neighbor spin-1 bilinear-biquadratic
Heisenberg model on the triangular lattice. In agreement with previous studies,
we find the ferromagnetic, 120 degree magnetically ordered, ferroquadrupolar
and antiferroquadrupolar phases, and confirm that all corresponding phase
transitions are first order. Moreover, we provide an accurate estimate of the
location of the ferroquadrupolar to 120 degree magnetically ordered phase
transition, thereby fully establishing the phase diagram. Also, we do not
encounter any signs of the existence of a quantum paramagnetic phase. In
particular, contrary to the equivalent square lattice model, we demonstrate
that on the triangular lattice the one-dimensional Haldane phase does not reach
all the way up to the two-dimensional limit. Finally, we investigate the
possibility of an intermediate partially-magnetic partially-quadrupolar phase
close to , and we show that, also contrary to the square
lattice case, this phase is not present on the triangular lattice.Comment: 14 pages, 15 figures; v2: shortened section II.B and added a
paragraph to section IV.
Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
Spinless fermions on a honeycomb lattice provide a minimal realization of
lattice Dirac fermions. Repulsive interactions between nearest neighbors drive
a quantum phase transition from a Dirac semimetal to a charge-density-wave
state through a fermionic quantum critical point, where the coupling of Ising
order parameter to the Dirac fermions at low energy drastically affects the
quantum critical behavior. Encouraged by a recently discovery of absence of the
fermion sign problem in this model, we study the fermionic quantum critical
point using the continuous time quantum Monte Carlo method with worm sampling
technique. We estimate the transition point with the critical
exponents and . Compatible results for the
transition point are also obtained with infinite projected entangled-pair
states.Comment: Single column, 21 pages, appendix on worm updates and \pi-flux
lattic
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
Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study
In spite of their intrinsic one-dimensional nature matrix product states have
been systematically used to obtain remarkably accurate results for
two-dimensional systems. Motivated by basic entropic arguments favoring
projected entangled-pair states as the method of choice, we assess the relative
performance of infinite matrix product states and infinite projected
entangled-pair states on cylindrical geometries. By considering the Heisenberg
and half-filled Hubbard models on the square lattice as our benchmark cases, we
evaluate their variational energies as a function of both bond dimension as
well as cylinder width. In both examples we find crossovers at moderate
cylinder widths, i.e. for the largest bond dimensions considered we find an
improvement on the variational energies for the Heisenberg model by using
projected entangled-pair states at a width of about 11 sites, whereas for the
half-filled Hubbard model this crossover occurs at about 7 sites.Comment: 11 pages, 9 figure
Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms
We study the extent of the spin liquid phases in the Kitaev-Heisenberg model
using infinite Projected Entangled-Pair States tensor network ansatz wave
functions directly in the thermodynamic limit. To assess the accuracy of the
ansatz wave functions we perform benchmarks against exact results for the
Kitaev model and find very good agreement for various observables. In the case
of the Kitaev-Heisenberg model we confirm the existence of 6 different phases:
N\'eel, stripy, ferromagnetic, zigzag and two spin liquid phases. We find
finite extents for both spin liquid phases and discontinuous phase transitions
connecting them to symmetry-broken phases.Comment: 9 pages, 7 figures. Adjusted notation in equations 4-8. Added bond
labeling to lower panel in figure 1. Included missing acknowledgement
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