15 research outputs found
New easy-plane fixed points
We study fixed points of the easy-plane field theory by
combining quantum Monte Carlo simulations of lattice models of easy-plane
SU() superfluids with field theoretic renormalization group calculations, by
using ideas of deconfined criticality. From our simulations, we present
evidence that at small our lattice model has a first order phase transition
which progressively weakens as increases, eventually becoming continuous
for large values of . Renormalization group calculations in
dimensions provide an explanation of these results as arising due to the
existence of an that separates the fate of the flows with easy-plane
anisotropy. When the renormalization group flows to a discontinuity
fixed point and hence a first order transition arises. On the other hand, for
the flows are to a new easy-plane fixed point
that describes the quantum criticality in the lattice model at large . Our
lattice model at its critical point thus gives efficient numerical access to a
new strongly coupled gauge-matter field theory.Comment: 12 pages, 9 figure
First-order superfluid to valence bond solid phase transitions in easy-plane SU() magnets for small-
We consider the easy-plane limit of bipartite SU() Heisenberg Hamiltonians
which have a fundamental representation on one sublattice and the conjugate to
fundamental on the other sublattice. For the easy plane limit of the
SU(2) Heisenberg model is the well known quantum XY model of a lattice
superfluid. We introduce a logical method to generalize the quantum XY model to
arbitrary , which keeps the Hamiltonian sign-free. We show that these
quantum Hamiltonians have a world-line representation as the statistical
mechanics of certain tightly packed loop models of -colors in which
neighboring loops are disallowed from having the same color. In this loop
representation we design an efficient Monte Carlo cluster algorithm for our
model. We present extensive numerical results for these models on the two
dimensional square lattice, where we find the nearest neighbor model has
superfluid order for and valence-bond order for . By
introducing SU() easy-plane symmetric four-spin couplings we are able to
tune across the superfluid-VBS phase boundary for all . We present
clear evidence that this quantum phase transition is first order for and
, suggesting that easy-plane deconfined criticality runs away generically
to a first order transition for small-.Comment: 8 pages, 8 figures, 1 tabl
Quadrupolar quantum criticality on a fractal
We study the ground state ordering of quadrupolar ordered magnets as a
function of spin dilution probability on the triangular lattice. In sharp
contrast to the ordering of dipolar N\'eel magnets on percolating
clusters, we find that the quadrupolar magnets are quantum disordered at the
percolation threshold, . Further we find that long-range quadrupolar
order is present for all and vanishes first exactly at . Strong
evidence for scaling behavior close to points to an unusual quantum
criticality without fine tuning that arises from an interplay of quantum
fluctuations and randomness
R\'enyi entanglement entropy of critical SU() spin chains
We present a study of the scaling behavior of the R\'{e}nyi entanglement
entropy (REE) in SU() spin chain Hamiltonians, in which all the spins
transform under the fundamental representation. These SU() spin chains are
known to be quantum critical and described by a well known Wess-Zumino-Witten
(WZW) non-linear sigma model in the continuum limit. Numerical results from our
lattice Hamiltonian are obtained using stochastic series expansion (SSE)
quantum Monte Carlo for both closed and open boundary conditions. As expected
for this 1D critical system, the REE shows a logarithmic dependence on the
subsystem size with a prefector given by the central charge of the SU() WZW
model. We study in detail the sub-leading oscillatory terms in the REE under
both periodic and open boundaries. Each oscillatory term is associated with a
WZW field and decays as a power law with an exponent proportional to the
scaling dimension of the corresponding field. We find that the use of periodic
boundaries (where oscillations are less prominent) allows for a better estimate
of the central charge, while using open boundaries allows for a better estimate
of the scaling dimensions. For completeness we also present numerical data on
the thermal R\'{e}nyi entropy which equally allows for extraction of the
central charge.Comment: 8 pages, 13 figure
Reduction of the sign problem near in quantum Monte Carlo simulations
Building on a recent investigation of the Shastry-Sutherland model [S. Wessel
et al., Phys. Rev. B 98, 174432 (2018)], we develop a general strategy to
eliminate the Monte Carlo sign problem near the zero temperature limit in
frustrated quantum spin models. If the Hamiltonian of interest and the
sign-problem-free Hamiltonian---obtained by making all off-diagonal elements
negative in a given basis---have the same ground state and this state is a
member of the computational basis, then the average sign returns to one as the
temperature goes to zero. We illustrate this technique by studying the
triangular and kagome lattice Heisenberg antiferrromagnet in a magnetic field
above saturation, as well as the Heisenberg antiferromagnet on a modified
Husimi cactus in the dimer basis. We also provide detailed appendices on using
linear programming techniques to automatically generate efficient directed loop
updates in quantum Monte Carlo simulations.Comment: 11 pages, 9 figure
Diagnosing weakly first-order phase transitions by coupling to order parameters
The hunt for exotic quantum phase transitions described by emergent
fractionalized degrees of freedom coupled to gauge fields requires a precise
determination of the fixed point structure from the field theoretical side, and
an extreme sensitivity to weak first-order transitions from the numerical side.
Addressing the latter, we revive the classic definition of the order parameter
in the limit of a vanishing external field at the transition. We demonstrate
that this widely understood, yet so far unused approach provides a diagnostic
test for first-order versus continuous behavior that is distinctly more
sensitive than current methods. We first apply it to the family of -state
Potts models, where the nature of the transition is continuous for and
turns (weakly) first order for , using an infinite system matrix product
state implementation. We then employ this new approach to address the unsettled
question of deconfined quantum criticality in the N\'eel to valence
bond solid transition in two dimensions, focusing on the square lattice -
model. Our quantum Monte Carlo simulations reveal that both order parameters
remain finite at the transition, directly confirming a first-order scenario
with wide reaching implications in condensed matter and quantum field theory.Comment: Published versio
Universal features of entanglement entropy in the honeycomb Hubbard model
The entanglement entropy is a unique probe to reveal universal features of
strongly interacting many-body systems. In two or more dimensions these
features are subtle, and detecting them numerically requires extreme precision,
a notoriously difficult task. This is especially challenging in models of
interacting fermions, where many such universal features have yet to be
observed. In this paper we tackle this challenge by introducing a new method to
compute the R\'enyi entanglement entropy in auxiliary-field quantum Monte Carlo
simulations, where we treat the entangling region itself as a stochastic
variable. We demonstrate the efficiency of this method by extracting, for the
first time, universal subleading logarithmic terms in a two dimensional model
of interacting fermions, focusing on the honeycomb Hubbard model at . We
detect the universal corner contribution due to gapless fermions throughout the
Dirac semi-metal phase and at the Gross-Neveu-Yukawa critical point, as well as
the universal Goldstone mode contribution in the antiferromagnetic Mott
insulating phase
Kagome model for a Z(2) quantum spin liquid
We present a study of a simple model antiferromagnet consisting of a sum of nearest-neighbor SO(N) singlet projectors on the kagome lattice. Our model shares some features with the popular S = 1/2 kagome antiferromagnet but is specifically designed to be free of the sign problem of quantum Monte Carlo. In our numerical analysis, we find as a function of N a quadrupolar magnetic state and a wide range of a quantum spin liquid. A solvable large-N generalization suggests that the quantum spin liquid in our original model is a gapped Z(2) topological phase. Supporting this assertion, a numerical study of the entanglement entropy in the sign free model shows a quantized topological contribution