72 research outputs found
Dynamic scaling of topological ordering in classical systems
We analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in two and three dimensions. We first consider the three-dimensional Z2 (Ising) lattice gauge model, which exhibits a continuous topological phase transition at finite temperature. We show that a generalized Kibble-Zurek scaling ansatz applies to this transition, in spite of the absence of a local order parameter. We find perimeter-law scaling of the magnitude of a nonlocal order parameter (defined using Wilson loops) and a dynamic exponent z=2.70±0.03, the latter in good agreement with previous results for the equilibrium dynamics (autocorrelations). We then study systems where (topological) order forms only at zero temperature - the Ising chain, the two-dimensional Z2 gauge model, and a three-dimensional star model (another variant of the Z2 gauge model). In these systems the correlation length diverges exponentially, in a way that is nonsmooth as a finite-size system approaches the zero temperature state. We show that the Kibble-Zurek theory does not apply in any of these systems. Instead, the dynamics can be understood in terms of diffusion and annihilation of topological defects, which we use to formulate a scaling theory in good agreement with our simulation results. We also discuss the effect of open boundaries where defect annihilation competes with a faster process of evaporation at the surface
Field theories of paramagnetic Mott insulators
This is a summary of a central argument in recent review articles by the
author (cond-mat/0109419, cond-mat/0211005, and cond-mat/0211027). An effective
field theory is derived for the low energy spin singlet excitations in a
paramagnetic Mott insulator with collinear spin correlations.Comment: 12 pages, 4 figures, Proceedings of the International Conference on
Theoretical Physics, Paris, UNESCO, July 200
Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
The Landau paradigm of classifying phases by broken symmetries was
demonstrated to be incomplete when it was realized that different quantum Hall
states could only be distinguished by more subtle, topological properties.
Today, the role of topology as an underlying description of order has branched
out to include topological band insulators, and certain featureless gapped Mott
insulators with a topological degeneracy in the groundstate wavefunction.
Despite intense focus, very few candidates for these topologically ordered
"spin liquids" exist. The main difficulty in finding systems that harbour spin
liquid states is the very fact that they violate the Landau paradigm, making
conventional order parameters non-existent. Here, we uncover a spin liquid
phase in a Bose-Hubbard model on the kagome lattice, and measure its
topological order directly via the topological entanglement entropy. This is
the first smoking-gun demonstration of a non-trivial spin liquid, identified
through its entanglement entropy as a gapped groundstate with emergent Z2 gauge
symmetry.Comment: 4+ pages, 3 figure
Quantum dimer models and exotic orders
We discuss how quantum dimer models may be used to provide "proofs of
principle" for the existence of exotic magnetic phases in quantum spin systems.Comment: 12 pages, 6 figures. Contributed talk at the PITP-Les Houches Summer
School on "Quantum Magnetism", June 200
Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
A spin liquid is a novel quantum state of matter with no conventional order
parameter where a finite charge gap exists even though the band theory would
predict metallic behavior. Finding a stable spin liquid in two or higher
spatial dimensions is one of the most challenging and debated issues in
condensed matter physics. Very recently, it has been reported that a model of
graphene, i.e., the Hubbard model on the honeycomb lattice, can show a spin
liquid ground state in a wide region of the phase diagram, between a semi-metal
(SM) and an antiferromagnetic insulator (AFMI). Here, by performing numerically
exact quantum Monte Carlo simulations, we extend the previous study to much
larger clusters (containing up to 2592 sites), and find, if any, a very weak
evidence of this spin liquid region. Instead, our calculations strongly
indicate a direct and continuous quantum phase transition between SM and AFMI.Comment: 15 pages with 7 figures and 9 tables including supplementary
information, accepted for publication in Scientific Report
Single and two-particle energy gaps across the disorder-driven superconductor-insulator transition
The competition between superconductivity and localization raises profound
questions in condensed matter physics. In spite of decades of research, the
mechanism of the superconductor-insulator transition (SIT) and the nature of
the insulator are not understood. We use quantum Monte Carlo simulations that
treat, on an equal footing, inhomogeneous amplitude variations and phase
fluctuations, a major advance over previous theories. We gain new microscopic
insights and make testable predictions for local spectroscopic probes. The
energy gap in the density of states survives across the transition, but
coherence peaks exist only in the superconductor. A characteristic pseudogap
persists above the critical disorder and critical temperature, in contrast to
conventional theories. Surprisingly, the insulator has a two-particle gap scale
that vanishes at the SIT, despite a robust single-particle gap.Comment: 7 pages, 5 figures (plus supplement with 4 pages, 5 figures
Fermionic response from fractionalization in an insulating two-dimensional magnet
Conventionally ordered magnets possess bosonic elementary excitations, called
magnons. By contrast, no magnetic insulators in more than one dimension are
known whose excitations are not bosons but fermions. Theoretically, some
quantum spin liquids (QSLs) -- new topological phases which can occur when
quantum fluctuations preclude an ordered state -- are known to exhibit Majorana
fermions as quasiparticles arising from fractionalization of spins. Alas,
despite much searching, their experimental observation remains elusive. Here,
we show that fermionic excitations are remarkably directly evident in
experimental Raman scattering data across a broad energy and temperature range
in the two-dimensional material -RuCl. This shows the importance of
magnetic materials as hosts of Majorana fermions. In turn, this first
systematic evaluation of the dynamics of a QSL at finite temperature emphasizes
the role of excited states for detecting such exotic properties associated with
otherwise hard-to-identify topological QSLs.Comment: 5 pages, 3 figure
Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
The presence of long-range quantum spin correlations underlies a variety of
physical phenomena in condensed matter systems, potentially including
high-temperature superconductivity. However, many properties of exotic strongly
correlated spin systems (e.g., spin liquids) have proved difficult to study, in
part because calculations involving N-body entanglement become intractable for
as few as N~30 particles. Feynman divined that a quantum simulator - a
special-purpose "analog" processor built using quantum particles (qubits) -
would be inherently adept at such problems. In the context of quantum
magnetism, a number of experiments have demonstrated the feasibility of this
approach. However, simulations of quantum magnetism allowing controlled,
tunable interactions between spins localized on 2D and 3D lattices of more than
a few 10's of qubits have yet to be demonstrated, owing in part to the
technical challenge of realizing large-scale qubit arrays. Here we demonstrate
a variable-range Ising-type spin-spin interaction J_ij on a naturally occurring
2D triangular crystal lattice of hundreds of spin-1/2 particles (9Be+ ions
stored in a Penning trap), a computationally relevant scale more than an order
of magnitude larger than existing experiments. We show that a spin-dependent
optical dipole force can produce an antiferromagnetic interaction J_ij ~
1/d_ij^a, where a is tunable over 0<a<3; d_ij is the distance between spin
pairs. These power-laws correspond physically to infinite-range (a=0),
Coulomb-like (a=1), monopole-dipole (a=2) and dipole-dipole (a=3) couplings.
Experimentally, we demonstrate excellent agreement with theory for 0.05<a<1.4.
This demonstration coupled with the high spin-count, excellent quantum control
and low technical complexity of the Penning trap brings within reach simulation
of interesting and otherwise computationally intractable problems in quantum
magnetism.Comment: 10 pages, 10 figures; article plus Supplementary Material
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