53 research outputs found
Phases and phase transitions in a U(1) × U(1) system with θ = 2π/3 mutual statistics
We study a U(1) × U(1) system with short-range interactions and mutual θ = 2π/3 statistics in (2+1)
dimensions. We are able to reformulate the model to eliminate the sign problem and perform a Monte Carlo
study. We find a phase diagram containing a phase with only small loops and two phases with one species of
proliferated loop. We also find a phase where both species of loop condense, but without any gapless modes.
Lastly, when the energy cost of loops becomes small, we find a phase that is a condensate of bound states, each
made up of three particles of one species and a vortex of the other. We define several exact reformulations of the
model that allow us to precisely describe each phase in terms of gapped excitations. We propose field-theoretic
descriptions of the phases and phase transitions, which are particularly interesting on the “self-dual” line where
both species have identical interactions. We also define irreducible responses useful for describing the phases
Monte Carlo Study of a U(1)xU(1) system with \pi-statistical Interaction
We study a system with two species of loops with mutual
-statistics in (2+1) dimensions. We are able to reformulate the model in a
way that can be studied by Monte Carlo and we determine the phase diagram. In
addition to a phase with no loops, we find two phases with only one species of
loop proliferated. The model has a self-dual line, a segment of which separates
these two phases. Everywhere on the segment, we find the transition to be
first-order, signifying that the two loop systems behave as immiscible fluids
when they are both trying to condense. Moving further along the self-dual line,
we find a phase where both loops proliferate, but they are only of even
strength, and therefore avoid the statistical interactions. We study another
model which does not have this phase, and also find first-order behavior on the
self-dual segment.Comment: 4 pages, 5 figure
Many body localization and thermalization: insights from the entanglement spectrum
We study the entanglement spectrum in the many body localizing and
thermalizing phases of one and two dimensional Hamiltonian systems, and
periodically driven `Floquet' systems. We focus on the level statistics of the
entanglement spectrum as obtained through numerical diagonalization, finding
structure beyond that revealed by more limited measures such as entanglement
entropy. In the thermalizing phase the entanglement spectrum obeys level
statistics governed by an appropriate random matrix ensemble. For Hamiltonian
systems this can be viewed as evidence in favor of a strong version of the
eigenstate thermalization hypothesis (ETH). Similar results are also obtained
for Floquet systems, where they constitute a result `beyond ETH', and show that
the corrections to ETH governing the Floquet entanglement spectrum have
statistical properties governed by a random matrix ensemble. The particular
random matrix ensemble governing the Floquet entanglement spectrum depends on
the symmetries of the Floquet drive, and therefore can depend on the choice of
origin of time. In the many body localized phase the entanglement spectrum is
also found to show level repulsion, following a semi-Poisson distribution (in
contrast to the energy spectrum, which follows a Poisson distribution). This
semi-Poisson distribution is found to come mainly from states at high
entanglement energies. The observed level repulsion only occurs for interacting
localized phases. We also demonstrate that equivalent results can be obtained
by calculating with a single typical eigenstate, or by averaging over a
microcanonical energy window - a surprising result in the localized phase. This
discovery of new structure in the pattern of entanglement of localized and
thermalizing phases may open up new lines of attack on many body localization,
thermalization, and the localization transition.Comment: 17 pages, 20 figure
Composite fermions in bands with N-fold rotational symmetry
We study the effect of band anisotropy with discrete rotational symmetry
(where ) in the quantum Hall regime of two-dimensional electron
systems. We focus on the composite Fermi liquid (CFL) at half filling of the
lowest Landau level. We find that the magnitude of anisotropy transferred to
the composite fermions decreases very rapidly with . We demonstrate this by
performing density matrix normalization group calculations on the CFL, and
comparing the anisotropy of the composite fermion Fermi contour with that of
the (non-interacting) electron Fermi contour at zero magnetic field. We also
show that the effective interaction between the electrons after projecting into
a single Landau level is much less anisotropic than the band, a fact which does
not depend on filling and thus has implications for other quantum Hall states
as well. Our results confirm experimental observations on anisotropic bands
with warped Fermi contours, where the only detectable effect on the composite
Fermi contour is an elliptical distortion ().Comment: 6 pages + bibliography, 5 figure
Connection between Fermi contours of zero-field electrons and composite fermions in two-dimensional systems
We investigate the relation between the Fermi sea (FS) of zero-field carriers
in two-dimensional systems and the FS of the corresponding composite fermions
which emerge in a high magnetic field at filling , as the
kinetic energy dispersion is varied. We study cases both with and without
rotational symmetry, and find that there is generally no straightforward
relation between the geometric shapes and topologies of the two FSs. In
particular, we show analytically that the composite Fermi liquid (CFL) is
completely insensitive to a wide range of changes to the zero-field dispersion
which preserve rotational symmetry, including ones that break the zero-field FS
into multiple disconnected pieces. In the absence of rotational symmetry, we
show that the notion of `valley pseudospin' in many-valley systems is
generically not transferred to the CFL, in agreement with experimental
observations. We also discuss how a rotationally symmetric band structure can
induce a reordering of the Landau levels, opening interesting possibilities of
observing higher-Landau-level physics in the high-field regime.Comment: 7 pages + references, 7 figures. Added many-body DMRG calculatio
Characterizing the many-body localization transition through the entanglement spectrum
We numerically explore the many body localization (MBL) transition through
the lens of the {\it entanglement spectrum}. While a direct transition from
localization to thermalization is believed to obtain in the thermodynamic limit
(the exact details of which remain an open problem), in finite system sizes
there exists an intermediate `quantum critical' regime. Previous numerical
investigations have explored the crossover from thermalization to criticality,
and have used this to place a numerical {\it lower} bound on the critical
disorder strength for MBL. A careful analysis of the {\it high energy} part of
the entanglement spectrum (which contains universal information about the
critical point) allows us to make the first ever observation in exact numerics
of the crossover from criticality to MBL and hence to place a numerical {\it
upper bound} on the critical disorder strength for MBL.Comment: 4 pages+appendi
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