110 research outputs found
Quantum Monte Carlo simulations in the trimer basis:First-order transitions and thermal critical points in frustrated trilayer magnets
The phase diagrams of highly frustrated quantum spin systems can exhibit
first-order quantum phase transitions and thermal critical points even in the
absence of any long-ranged magnetic order. However, all unbiased numerical
techniques for investigating frustrated quantum magnets face significant
challenges, and for generic quantum Monte Carlo methods the challenge is the
sign problem. Here we report on a general quantum Monte Carlo approach with a
loop-update scheme that operates in any basis, and we show that, with an
appropriate choice of basis, it allows us to study a frustrated model of
coupled spin-1/2 trimers: simulations of the trilayer Heisenberg
antiferromagnet in the spin-trimer basis are sign-problem-free when the
intertrimer couplings are fully frustrated. This model features a first-order
quantum phase transition, from which a line of first-order transitions emerges
at finite temperatures and terminates in a thermal critical point. The trimer
unit cell hosts an internal degree of freedom that can be controlled to induce
an extensive entropy jump at the quantum transition, which alters the shape of
the first-order line. We explore the consequences for the thermal properties in
the vicinity of the critical point, which include profound changes in the lines
of maxima defined by the specific heat. Our findings reveal trimer quantum
magnets as fundamental systems capturing in full the complex thermal physics of
the strongly frustrated regime.Comment: 27 pages, 10 figures, Resubmission to SciPos
Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations
We investigate the minus-sign problem that afflicts quantum Monte Carlo (QMC)
simulations of frustrated quantum spin systems, focusing on spin S=1/2, two
spatial dimensions, and the extended Shastry-Sutherland model. We show that
formulating the Hamiltonian in the diagonal dimer basis leads to a sign problem
that becomes negligible at low temperatures for small and intermediate values
of the ratio of the inter- and intradimer couplings. This is a consequence of
the fact that the product state of dimer singlets is the exact ground state
both of the extended Shastry-Sutherland model and of a corresponding
"sign-problem-free" model, obtained by changing the signs of all positive
off-diagonal matrix elements in the dimer basis. By exploiting this insight, we
map the sign problem throughout the extended parameter space from the
Shastry-Sutherland to the fully frustrated bilayer model and compare it with
the phase diagram computed by tensor-network methods. We use QMC to compute
with high accuracy the temperature dependence of the magnetic specific heat and
susceptibility of the Shastry-Sutherland model for large systems up to a
coupling ratio of 0.526(1) and down to zero temperature. For larger coupling
ratios, our QMC results assist us in benchmarking the evolution of the
thermodynamic properties by systematic comparison with exact diagonalization
calculations and interpolated high-temperature series expansions.Comment: 13 pages including 10 figures; published version with minor changes
and correction
Entanglement Entropy of Random Fractional Quantum Hall Systems
The entanglement entropy of the and quantum Hall
states in the presence of short range random disorder has been calculated by
direct diagonalization. A microscopic model of electron-electron interaction is
used, electrons are confined to a single Landau level and interact with long
range Coulomb interaction. For very weak disorder, the values of the
topological entanglement entropy are roughly consistent with expected
theoretical results. By considering a broader range of disorder strengths, the
fluctuation in the entanglement entropy was studied in an effort to detect
quantum phase transitions. In particular, there is a clear signature of a
transition as a function of the disorder strength for the state.
Prospects for using the density matrix renormalization group to compute the
entanglement entropy for larger system sizes are discussed.Comment: 29 pages, 16 figures; fixed figures and figure captions; revised
fluctuation calculation
Comment on "Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice" by Poletti D. et al
In a recent letter [D. Poletti et al., EPL 93, 37008 (2011)] a model of
attractive spinless fermions on the honeycomb lattice at half filling has been
studied by mean-field theory, where distinct homogenous phases at rather large
attraction strength , separated by (topological) phase transitions,
have been predicted. In this comment we argue that without additional
interactions the ground states in these phases are not stable against phase
separation. We determine the onset of phase separation at half filling
by means of infinite projected entangled-pair states
(iPEPS) and exact diagonalization.Comment: 2 pages, 1 figur
Tensor network states and geometry
Tensor network states are used to approximate ground states of local
Hamiltonians on a lattice in D spatial dimensions. Different types of tensor
network states can be seen to generate different geometries. Matrix product
states (MPS) in D=1 dimensions, as well as projected entangled pair states
(PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the
lattice model; in contrast, the multi-scale entanglement renormalization ansatz
(MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on
homogeneous tensor networks, where all the tensors in the network are copies of
the same tensor, and argue that certain structural properties of the resulting
many-body states are preconditioned by the geometry of the tensor network and
are therefore largely independent of the choice of variational parameters.
Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for
D=1 systems is seen to be determined by the structure of geodesics in the
physical and holographic geometries, respectively; whereas the asymptotic
scaling of entanglement entropy is seen to always obey a simple boundary law --
that is, again in the relevant geometry. This geometrical interpretation offers
a simple and unifying framework to understand the structural properties of, and
helps clarify the relation between, different tensor network states. In
addition, it has recently motivated the branching MERA, a generalization of the
MERA capable of reproducing violations of the entropic boundary law in D>1
dimensions.Comment: 18 pages, 18 figure
Many body physics from a quantum information perspective
The quantum information approach to many body physics has been very
successful in giving new insight and novel numerical methods. In these lecture
notes we take a vertical view of the subject, starting from general concepts
and at each step delving into applications or consequences of a particular
topic. We first review some general quantum information concepts like
entanglement and entanglement measures, which leads us to entanglement area
laws. We then continue with one of the most famous examples of area-law abiding
states: matrix product states, and tensor product states in general. Of these,
we choose one example (classical superposition states) to introduce recent
developments on a novel quantum many body approach: quantum kinetic Ising
models. We conclude with a brief outlook of the field.Comment: Lectures from the Les Houches School on "Modern theories of
correlated electron systems". Improved version new references adde
A quantum magnetic analogue to the critical point of water
At the familiar liquid-gas phase transition in water, the density jumps
discontinuously at atmospheric pressure, but the line of these first-order
transitions defined by increasing pressures terminates at the critical point, a
concept ubiquitous in statistical thermodynamics. In correlated quantum
materials, a critical point was predicted and measured terminating the line of
Mott metal-insulator transitions, which are also first-order with a
discontinuous charge density. In quantum spin systems, continuous quantum phase
transitions (QPTs) have been investigated extensively, but discontinuous QPTs
have received less attention. The frustrated quantum antiferromagnet
SrCu(BO) constitutes a near-exact realization of the paradigmatic
Shastry-Sutherland model and displays exotic phenomena including magnetization
plateaux, anomalous thermodynamics and discontinuous QPTs. We demonstrate by
high-precision specific-heat measurements under pressure and applied magnetic
field that, like water, the pressure-temperature phase diagram of
SrCu(BO) has an Ising critical point terminating a first-order
transition line, which separates phases with different densities of magnetic
particles (triplets). We achieve a quantitative explanation of our data by
detailed numerical calculations using newly-developed finite-temperature
tensor-network methods. These results open a new dimension in understanding the
thermodynamics of quantum magnetic materials, where the anisotropic spin
interactions producing topological properties for spintronic applications drive
an increasing focus on first-order QPTs.Comment: 8+4 pages, 4+3 figure
Study of solid 4He in two dimensions. The issue of zero-point defects and study of confined crystal
Defects are believed to play a fundamental role in the supersolid state of
4He. We report on studies by exact Quantum Monte Carlo (QMC) simulations at
zero temperature of the properties of solid 4He in presence of many vacancies,
up to 30 in two dimensions (2D). In all studied cases the crystalline order is
stable at least as long as the concentration of vacancies is below 2.5%. In the
2D system for a small number, n_v, of vacancies such defects can be identified
in the crystalline lattice and are strongly correlated with an attractive
interaction. On the contrary when n_v~10 vacancies in the relaxed system
disappear and in their place one finds dislocations and a revival of the
Bose-Einstein condensation. Thus, should zero-point motion defects be present
in solid 4He, such defects would be dislocations and not vacancies, at least in
2D. In order to avoid using periodic boundary conditions we have studied the
exact ground state of solid 4He confined in a circular region by an external
potential. We find that defects tend to be localized in an interfacial region
of width of about 15 A. Our computation allows to put as upper bound limit to
zero--point defects the concentration 0.003 in the 2D system close to melting
density.Comment: 17 pages, accepted for publication in J. Low Temp. Phys., Special
Issue on Supersolid
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