2,904 research outputs found
The many-body localization phase transition
We use exact diagonalization to explore the many-body localization transition
in a random-field spin-1/2 chain. We examine the correlations within each
many-body eigenstate, looking at all high-energy states and thus effectively
working at infinite temperature. For weak random field the eigenstates are
thermal, as expected in this nonlocalized, "ergodic" phase. For strong random
field the eigenstates are localized, with only short-range entanglement. We
roughly locate the localization transition and examine some of its finite-size
scaling, finding that this quantum phase transition at nonzero temperature
might be showing infinite-randomness scaling with a dynamic critical exponent
.Comment: 7 pages, 8 figures. Extended version of arXiv:1003.2613v
Rare region effects dominate weakly disordered 3D Dirac points
We study three-dimensional Dirac fermions with weak finite-range scalar
potential disorder. In the clean system, the density of states vanishes
quadratically at the Dirac point. Disorder is known to be perturbatively
irrelevant, and previous theoretical work has assumed that the Dirac semimetal
phase, characterized by a vanishing density of states, survives at weak
disorder, with a finite disorder phase transition to a diffusive metal with a
non-vanishing density of states. In this paper we show that nonperturbative
effects from rare regions, which are missed by conventional disorder-averaged
calculations, instead give rise to a nonzero density of states for any nonzero
disorder. Thus, there is no Dirac semimetal phase at non-zero disorder. The
results are established both by a heuristic scaling argument and via a
systematic saddle point analysis. We also discuss transport near the Dirac
point. At the Dirac point, we argue that transport is diffusive, and proceeds
via hopping between rare resonances. As one moves in chemical potential away
from the Dirac point, there are interesting intermediate-energy regimes where
the rare regions produce scattering resonances that determine the DC
conductivity. We derive a scaling theory of transport near disordered 3D Dirac
points. We also discuss the interplay of disorder with attractive interactions
at the Dirac point, and the resulting granular superconducting and Bose glass
phases. Our results are relevant for all 3D systems with Dirac points,
including Weyl semimetals.Comment: Expanded version of 1307.3252 with many new results, including a new
section showing how the results may be derived using a systematic saddle
point calculatio
Superconductivity of disordered Dirac fermions
We study the effect of disorder on massless, spinful Dirac fermions in two
spatial dimensions with attractive interactions, and show that the combination
of disorder and attractive interactions is deadly to the Dirac semimetal phase.
First, we derive the zero temperature phase diagram of a clean Dirac fermion
system with tunable doping level ({\mu}) and attraction strength (g). We show
that it contains two phases: a superconductor and a Dirac semimetal. Then, we
show that arbitrarily weak disorder destroys the Dirac semimetal, turning it
into a superconductor. We discuss the strength of the superconductivity for
both long range and short range disorder. For long range disorder, the
superconductivity is exponentially weak in the disorder strength. For short
range disorder, a uniform mean field analysis predicts that superconductivity
should be doubly exponentially weak in the disorder strength. However, a more
careful treatment of mesoscopic fluctuations suggests that locally
superconducting puddles should form at a much higher temperature, and should
establish global phase coherence at a temperature that is only exponentially
small in weak disorder. We also discuss the effect of disorder on the quantum
critical point of the clean system, building in the effect of disorder through
a replica field theory. We show that disorder is a relevant perturbation to the
supersymmetric quantum critical point. We expect that in the presence of
attractive interactions, the flow away from the critical point ends up in the
superconducting phase, although firm conclusions cannot be drawn since the
renormalization group analysis flows to strong coupling. We argue that although
we expect the quantum critical point to get buried under a superconducting
phase, signatures of the critical point may be visible in the finite
temperature quantum critical regime.Comment: Added some discussion, particularly pertaining to proximity effec
Non-equilibrium dynamic critical scaling of the quantum Ising chain
We solve for the time-dependent finite-size scaling functions of the 1D
transverse-field Ising chain during a linear-in-time ramp of the field through
the quantum critical point. We then simulate Mott-insulating bosons in a tilted
potential, an experimentally-studied system in the same equilibrium
universality class, and demonstrate that universality holds for the dynamics as
well. We find qualitatively athermal features of the scaling functions, such as
negative spin correlations, and show that they should be robustly observable
within present cold atom experiments.Comment: 4 pages + 2 page supplemen
Diagnosing Deconfinement and Topological Order
Topological or deconfined phases are characterized by emergent, weakly
fluctuating, gauge fields. In condensed matter settings they inevitably come
coupled to excitations that carry the corresponding gauge charges which
invalidate the standard diagnostic of deconfinement---the Wilson loop. Inspired
by a mapping between symmetric sponges and the deconfined phase of the
gauge theory, we construct a diagnostic for deconfinement that has the
interpretation of a line tension. One operator version of this diagnostic turns
out to be the Fredenhagen-Marcu order parameter known to lattice gauge
theorists and we show that a different version is best suited to condensed
matter systems. We discuss generalizations of the diagnostic, use it to
establish the existence of finite temperature topological phases in
dimensions and show that multiplets of the diagnostic are useful in settings
with multiple phases such as gauge theories with charge matter.
[Additionally we present an exact reduction of the partition function of the
toric code in general dimensions to a well studied problem.]Comment: 11 pages, several figure
Permutation-Symmetric Multicritical Points in Random Antiferromagnetic Spin Chains
The low-energy properties of a system at a critical point may have additional
symmetries not present in the microscopic Hamiltonian. This letter presents the
theory of a class of multicritical points that provide an interesting example
of this in the phase diagrams of random antiferromagnetic spin chains. One case
provides an analytic theory of the quantum critical point in the random
spin-3/2 chain, studied in recent work by Refael, Kehrein and Fisher
(cond-mat/0111295).Comment: Revtex, 4 pages (2 column format), 2 eps figure
Spin-nematic order in the frustrated pyrochlore-lattice quantum rotor model
As an example of ordering due to quantum fluctuations, we examine the
nearest-neighbor antiferromagnetic quantum O(n) rotor model on the pyrochlore
lattice. Classically, this system remains disordered even at zero temperature;
we find that adding quantum fluctuations induces an ordered phase that survives
to positive temperature, and we determine how its phase diagram scales with the
coupling constant and the number of spin components. We demonstrate, using
quantum Monte Carlo simulations, that this phase has long-range spin-nematic
order, and that the phase transition into it appears to be first order.Comment: 10 pages, 8 figure
Competing density-wave orders in a one-dimensional hard-boson model
We describe the zero-temperature phase diagram of a model of bosons,
occupying sites of a linear chain, which obey a hard-exclusion constraint: any
two nearest-neighbor sites may have at most one boson. A special case of our
model was recently proposed as a description of a ``tilted'' Mott insulator of
atoms trapped in an optical lattice. Our quantum Hamiltonian is shown to
generate the transfer matrix of Baxter's hard-square model. Aided by exact
solutions of a number of special cases, and by numerical studies, we obtain a
phase diagram containing states with long-range density-wave order with period
2 and period 3, and also a floating incommensurate phase. Critical theories for
the various quantum phase transitions are presented. As a byproduct, we show
how to compute the Luttinger parameter in integrable theories with
hard-exclusion constraints.Comment: 16 page
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