22,268 research outputs found
Bound states of three fermions forming symmetry-protected topological phases
We propose a simple theoretical construction of certain short-range entangled
phases of interacting fermions, by putting the bound states of three fermions
(which we refer to as clustons) into topological bands. We give examples in two
and three dimensions, and show that they are distinct from any free fermion
state. We further argue that these states can be viewed as combinations of
certain free fermion topological states and bosonic symmetry-protected
topological (SPT) states. This provides a conceptually simple understanding of
various SPT phases, and the possibility of realizing them in cold atom systems.
New parton constructions of these SPT phases in purely bosonic systems are
proposed. We also discuss a related anomaly in two dimensional Dirac theories,
which is the gravitational analogue of the parity anomaly.Comment: 4+4 pages, 3 figure
Schr\"odinger Soliton from Lorentzian Manifolds
In this paper, we introduce a new notion named as Schr\"odinger soliton.
So-called Schr\"odinger solitons are defined as a class of special solutions to
the Schr\"odinger flow equation from a Riemannian manifold or a Lorentzian
manifold into a K\"ahler manifold . If the target manifold admits a
Killing potential, then the Schr\"odinger soliton is just a harmonic map with
potential from into . Especially, if the domain manifold is a Lorentzian
manifold, the Schr\"odinger soliton is a wave map with potential into . Then
we apply the geometric energy method to this wave map system, and obtain the
local well-posedness of the corresponding Cauchy problem as well as global
existence in 1+1 dimension. As an application, we obtain the existence of
Schr\"odinger soliton of the hyperbolic Ishimori system.Comment: 22 pages, with lower regularity of the initial data required in the
revised version
Composite fermi liquids in the lowest Landau level
We study composite fermi liquid (CFL) states in the lowest Landau level (LLL)
limit at a generic filling . We begin with the old
observation that, in compressible states, the composite fermion in the lowest
Landau level should be viewed as a charge-neutral particle carrying vorticity.
This leads to the absence of a Chern-Simons term in the effective theory of the
CFL. We argue here that instead a Berry curvature should be enclosed by the
fermi surface of composite fermions, with the total Berry phase fixed by the
filling fraction . We illustrate this point with the CFL of
fermions at filling fractions and (single and two-component) bosons
at . The Berry phase leads to sharp consequences in the transport
properties including thermal and spin Hall conductances, which in the RPA
approximation are distinct from the standard Halperin-Lee-Read predictions. We
emphasize that these results only rely on the LLL limit, and do not require
particle-hole symmetry, which is present microscopically only for fermions at
. Nevertheless, we show that the existing LLL theory of the composite
fermi liquid for bosons at does have an emergent particle-hole
symmetry. We interpret this particle-hole symmetry as a transformation between
the empty state at and the boson integer quantum hall state at .
This understanding enables us to define particle-hole conjugates of various
bosonic quantum Hall states which we illustrate with the bosonic Jain and
Pfaffian states. The bosonic particle-hole symmetry can be realized exactly on
the surface of a three-dimensional boson topological insulator. We also show
that with the particle-hole and spin rotation symmetries, there is no
gapped topological phase for bosons at .Comment: 16 pages, 1 figure, new version with minor change
Dual Dirac liquid on the surface of the electron topological insulator
We discuss a non-fermi liquid gapless metallic surface state of the
topological band insulator. It has an odd number of gapless Dirac fermions
coupled to a non-compact U(1) gauge field. This can be viewed as a vortex dual
to the conventional Dirac fermion surface state. This surface duality is a
reflection of a bulk dual description discussed recently for the gauged
topological insulator. All the other known surface states can be conveniently
accessed from the dual Dirac liquid, including the surface quantum hall state,
the Fu-Kane superconductor, the gapped symmetric topological order and the
"composite Dirac liquid". We also discuss the physical properties of the dual
Dirac liquid, and its connection to the half-filled Landau level.Comment: 5+2 page
Time-reversal symmetric U(1) quantum spin liquids
We study possible quantum spin liquids in three dimensions with
time-reversal symmetry. We find a total of 7 families of such spin
liquids, distinguished by the properties of their emergent electric/magnetic
charges. We show how these spin liquids are related to each other. Two of these
classes admit nontrivial protected surface states which we describe. We show
how to access all of the 7 spin liquids through slave particle (parton)
constructions. We also provide intuitive loop gas descriptions of their ground
state wave functions. One of these phases is the `topological Mott insulator'
conventionally described as a topological insulator of an emergent fermionic
`spinon'. We show that this phase admits a remarkable dual description as a
topological insulator of emergent fermionic magnetic monopoles. This results in
a new (possibly natural) surface phase for the topological Mott insulator and a
new slave particle construction. We describe some of the continuous quantum
phase transitions between the different spin liquids. Each of these
seven families of states admits a finer distinction in terms of their surface
properties which we determine by combining these spin liquids with symmetry
protected topological phases. We discuss lessons for materials such as
pyrochlore quantum spin ices which may harbor a spin liquid. We suggest
the topological Mott insulator as a possible ground state in some range of
parameters for the quantum spin ice Hamiltonian.Comment: 25 pages, 11 figures, 1 tabl
Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
We synthesize and partly review recent developments relating the physics of
the half-filled Landau level in two dimensions to correlated surface states of
topological insulators in three dimensions. The latter are in turn related to
the physics of certain three dimensional quantum spin liquid states. The
resulting insights provide an interesting answer to the old question of how
particle-hole symmetry is realized in composite fermion liquids. Specifically
the metallic state at filling - described originally in
pioneering work by Halperin , Lee, and Read as a liquid of composite fermions -
was proposed recently by Son to be described by a particle-hole symmetric
effective field theory distinct from that in the prior literature. We show how
the relation to topological insulator surface states leads to a physical
understanding of the correctness of this proposal. We develop a simple picture
of the particle-hole symmetric composite fermion through a modification of
older pictures as electrically neutral "dipolar" particles. We revisit the
phenomenology of composite fermi liquids (with or without particle-hole
symmetry), and show that their heat/electrical transport dramatically violates
the conventional Wiedemann-Franz law but satisfies a modified one. We also
discuss the implications of these insights for finding physical realizations of
correlated topological insulator surfaces.Comment: 22 pages, 7 figures; (v2) Added some clarifications and corrected
typo
Interacting fermionic topological insulators/superconductors in three dimensions
Symmetry Protected Topological (SPT) phases are a minimal generalization of
the concept of topological insulators to interacting systems. In this paper we
describe the classification and properties of such phases for three
dimensional(3D) electronic systems with a number of different symmetries. For
symmetries representative of all classes in the famous 10-fold way of free
fermion topological insulators/superconductors, we determine the stability to
interactions. By combining with results on bosonic SPT phases we obtain a
classification of electronic 3D SPT phases for these symmetries. In cases with
a normal U(1) subgroup we show that this classification is complete. We
describe the non-trivial surface and bulk properties of these states. In
particular we discuss interesting correlated surface states that are not
captured in a free fermion description. We show that in many, but not all
cases, the surface can be gapped while preserving symmetry if it develops
intrinsic topological order.Comment: 14+1 pages, an erratum is added at the end, the original paper is
unchange
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