1,335 research outputs found
Topological Orders with Global Gauge Anomalies
By definition, the physics of the dimensional (dim) boundary of a
dim symmetry protected topological (SPT) state cannot be realized as
itself on a dim lattice. If the symmetry of the system is unitary, then a
formal way to determine whether a dim theory must be a boundary or not, is
to couple this theory to a gauge field (or to "gauge" its symmetry), and check
if there is a gauge anomaly. In this paper we discuss the following question:
can the boundary of a SPT state be driven into a fully gapped topological order
which preserves all the symmetries? We argue that if the gauge anomaly of the
boundary is "perturbative", then the boundary must remain gapless; while if the
boundary only has global gauge anomaly but no perturbative anomaly, then it is
possible to gap out the boundary by driving it into a topological state, when
. We will demonstrate this conclusion with two examples: (1) the
spin-1/2 chiral fermion with the well-known Witten's global anomaly, which is
the boundary of a topological superconductor with SU(2) or U(1) symmetry; and (2) the boundary of a topological superconductor
with the same symmetry. We show that these boundary systems can be driven into
a fully gapped topological order with topological degeneracy,
but this topological order cannot be future driven into a
trivial confined phase that preserves all the symmetries due to some special
properties of its topological defects.Comment: 12 page
Symmetry Protected Topological States of Interacting Fermions and Bosons
We study the classification of interacting fermionic and bosonic symmetry
protected topological (SPT) states. We define a SPT state as whether or not it
is separated from the trivial state through a bulk phase transition, which is a
general definition applicable to SPT states with or without spatial symmetries.
We show that in all dimensions short range interactions can reduce the
classification of free fermion SPT states, and we demonstrate these results by
making connection between fermionic and bosonic SPT states. We first
demonstrate that our formalism gives the correct classification for all the
known SPT states, with or without interaction, then we will generalize our
method to SPT states that involve the spatial inversion symmetry.Comment: 19 pages, 3 figure
Interacting Topological Superconductors and possible Origin of Chiral Fermions in the Standard Model
Motivated by the observation that the Standard Model of particle physics
(plus a right-handed neutrino) has precisely 16 Weyl fermions per generation,
we search for -dimensional chiral fermionic theories and chiral gauge
theories that can be regularized on a 3 dimensional spatial lattice when and
only when the number of flavors is an integral multiple of 16. All these
results are based on the observation that local interactions reduce the
classification of certain -dimensional topological superconductors from
to , which means that one of their
-dimensional boundaries can be gapped out by interactions without
breaking any symmetry when and only when the number of boundary chiral fermions
is an integral multiple of .Comment: 5 pages, 2 figure
Stable Gapless Bose Liquid Phases without any Symmetry
It is well-known that a stable algebraic spin liquid state (or equivalently
an algebraic Bose liquid (ABL) state) with emergent gapless photon excitations
can exist in quantum spin ice systems, or in a quantum dimer model on a
bipartite lattice. This photon phase is stable against any weak
perturbation without assuming any symmetry. Further works concluded that
certain lattice models give rise to more exotic stable algebraic Bose liquid
phases with graviton-like excitations. In this paper we will show how these
algebraic Bose liquid states can be generalized to stable phases with even more
exotic types of gapless excitations and then argue that these new phases are
stable against weak perturbations. We also explicitly show that these theories
have an (algebraic) topological ground state degeneracy on a torus, and
construct the corresponding topological invariants.Comment: 8 pages, 1 figur
"Self-Dual" Quantum Critical Point on the surface of Topological Insulator
In the last few years a lot of exotic and anomalous topological phases were
constructed by proliferating the vortex like topological defects on the surface
of the topological insulator (TI). In this work, rather than considering
topological phases at the boundary, we will study quantum critical points
driven by vortex like topological defects. In general we will discuss a
quantum phase transition described by the following field theory:
, with tuning
parameter , arbitrary integer , Dirac fermion and complex scalar
bosonic field which both couple to the same dynamical
noncompact U(1) gauge field . The physical meaning of these
quantities/fields will be explained in the text. We demonstrate that this
quantum critical point has a quasi self-dual nature. And at this quantum
critical point, various universal quantities such as the electrical
conductivity, and scaling dimension of gauge invariant operators can be
calculated systematically through a expansion, based on the observation
that the limit corresponds to an ordinary XY
transition.Comment: 5 pages, 2 figure
Disordered XYZ Spin Chain Simulations using the Spectrum Bifurcation Renormalization Group
We study the disordered XYZ spin chain using the recently developed Spectrum
Bifurcation Renormalization Group (SBRG) numerical method. With strong
disorder, the phase diagram consists of three many body localized (MBL) spin
glass phases. We argue that, with sufficiently strong disorder, these spin
glass phases are separated by marginally many-body localized (MBL) critical
lines. We examine the critical lines of this model by measuring the
entanglement entropy and Edwards-Anderson spin glass order parameter, and find
that the critical lines are characterized by an effective central charge
c'=ln2. Our data also suggests continuously varying critical exponents along
the critical lines. We also demonstrate how long-range mutual information can
distinguish these phases.Comment: 15 pages, 12 figure
Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group
We introduce the spectrum bifurcation renormalization group (SBRG) as a
generalization of the real-space renormalization group for the many-body
localized (MBL) system without truncating the Hilbert space. Starting from a
disordered many-body Hamiltonian in the full MBL phase, the SBRG flows to the
MBL fixed-point Hamiltonian, and generates the local conserved quantities and
the matrix product state representations for all eigenstates. The method is
applicable to both spin and fermion models with arbitrary interaction strength
on any lattice in all dimensions, as long as the models are in the MBL phase.
In particular, we focus on the interacting Majorana chain with strong
disorder, and map out its phase diagram using the entanglement entropy. The
SBRG flow also generates an entanglement holographic mapping, which duals the
MBL state to a fragmented holographic space decorated with small blackholes.Comment: 18 pages + 4 pages of appendixes and references, 20 figure
Topological number and Fermion Green's function of Strongly Interacting Topological Superconductors
It has been understood that short range interactions can reduce the
classification of topological superconductors in all dimensions. In this paper
we demonstrate by explicit calculations that when the topological phase
transition between two distinct phases in the noninteracting limit is gapped
out by interaction, the bulk fermion Green's function at the
"transition" approaches zero as at certain momentum
in the Brillouin zone.Comment: 5 pages, 1 figur
Many-Body Localization of Symmetry Protected Topological States
We address the following question: Which kinds of symmetry protected
topological (SPT) Hamiltonians can be many-body localized? That is, which
Hamiltonians with an SPT ground state have finite energy density excited states
which are all localized by disorder? Based on the observation that a finite
energy density state, if localized, can be viewed as the ground state of a
local Hamiltonian, we propose a simple (though possibly incomplete) rule for
many-body localization of SPT Hamiltonians: If the ground state and top state
(highest energy state) belong to the same SPT phase, then it is possible to
localize all the finite energy density states; If the ground and top state
belong to different SPT phases, then most likely there are some finite energy
density states which can not be fully localized. We will give concrete examples
of both scenarios. In some of these examples, we argue that interaction can
actually "assist" localization of finite energy density states, which is
counter-intuitive to what is usually expected.Comment: 5 pages 2 figure
Quantum Phase Transitions Between Bosonic Symmetry Protected Topological States Without Sign Problem: Nonlinear Sigma Model with a Topological Term
We propose a series of simple lattice interacting fermion models that we
demonstrate at low energy describe bosonic symmetry protected topological (SPT)
states and quantum phase transitions between them. This is because due to
interaction the fermions are gapped both at the boundary of the SPT states and
at the bulk quantum phase transition, thus these models at low energy can be
described completely by bosonic degrees of freedom. We show that the bulk of
these models is described by a Sp() principal chiral model with a
topological -term, whose boundary is described by a Sp() principal
chiral model with a Wess-Zumino-Witten term at level-1. The quantum phase
transition between SPT states in the bulk is tuned by a particular interaction
term, which corresponds to tuning in the field theory, and the phase
transition occurs at . The simplest version of these models with
is equivalent to the familiar O(4) nonlinear sigma model (NLSM) with a
topological term, whose boundary is a conformal field theory with
central charge . After breaking the O(4) symmetry to its subgroups, this
model can be viewed as bosonic SPT states with U(1), or symmetries, etc.
All these fermion models including the bulk quantum phase transitions can be
simulated with determinant Quantum Monte Carlo method without the sign problem.
Recent numerical results strongly suggests that the quantum disordered phase of
the O(4) NLSM with precisely is a stable conformal
field theory (CFT) with gapless bosonic modes.Comment: 10 pages, 3 figure
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