1,104 research outputs found
Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
We use the conformal bootstrap to perform a precision study of the operator
spectrum of the critical 3d Ising model. We conjecture that the 3d Ising
spectrum minimizes the central charge c in the space of unitary solutions to
crossing symmetry. Because extremal solutions to crossing symmetry are uniquely
determined, we are able to precisely reconstruct the first several Z2-even
operator dimensions and their OPE coefficients. We observe that a sharp
transition in the operator spectrum occurs at the 3d Ising dimension
Delta_sigma=0.518154(15), and find strong numerical evidence that operators
decouple from the spectrum as one approaches the 3d Ising point. We compare
this behavior to the analogous situation in 2d, where the disappearance of
operators can be understood in terms of degenerate Virasoro representations.Comment: 55 pages, many figures; v2 - refs and comments added, to appear in a
special issue of J.Stat.Phys. in memory of Kenneth Wilso
Supersonic quantum communication
When locally exciting a quantum lattice model, the excitation will propagate
through the lattice. The effect is responsible for a wealth of non-equilibrium
phenomena, and has been exploited to transmit quantum information through spin
chains. It is a commonly expressed belief that for local Hamiltonians, any such
propagation happens at a finite "speed of sound". Indeed, the Lieb-Robinson
theorem states that in spin models, all effects caused by a perturbation are
limited to a causal cone defined by a constant speed, up to exponentially small
corrections. In this work we show that for translationally invariant bosonic
models with nearest-neighbor interactions, this belief is incorrect: We prove
that one can encounter excitations which accelerate under the natural dynamics
of the lattice and allow for reliable transmission of information faster than
any finite speed of sound. The effect is only limited by the model's range of
validity (eventually by relativity). It also implies that in non-equilibrium
dynamics of strongly correlated bosonic models far-away regions may become
quickly entangled, suggesting that their simulation may be much harder than
that of spin chains even in the low energy sector.Comment: 4+3 pages, 1 figure, some material added, typographic error fixe
Mott Insulators, No-Double-Occupancy, and Non-Abelian Superconductivity
SU(4) dynamical symmetry is shown to imply a no-double-occupancy constraint
on the minimal symmetry description of antiferromagnetism and d-wave
superconductivity. This implies a maximum doping fraction of 1/4 for cuprates
and provides a microscopic critique of the projected SO(5) model. We propose
that SU(4) superconductors are representative of a class of compounds that we
term non-abelian superconductors. We further suggest that non-abelian
superconductors may exist having SU(4) symmetry and therefore cuprate-like
dynamics, but without d-wave hybridization.Comment: 4 pages, 2 figure
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
Conformal field theories have been long known to describe the fascinating
universal physics of scale invariant critical points. They describe continuous
phase transitions in fluids, magnets, and numerous other materials, while at
the same time sit at the heart of our modern understanding of quantum field
theory. For decades it has been a dream to study these intricate strongly
coupled theories nonperturbatively using symmetries and other consistency
conditions. This idea, called the conformal bootstrap, saw some successes in
two dimensions but it is only in the last ten years that it has been fully
realized in three, four, and other dimensions of interest. This renaissance has
been possible both due to significant analytical progress in understanding how
to set up the bootstrap equations and the development of numerical techniques
for finding or constraining their solutions. These developments have led to a
number of groundbreaking results, including world record determinations of
critical exponents and correlation function coefficients in the Ising and
models in three dimensions. This article will review these exciting
developments for newcomers to the bootstrap, giving an introduction to
conformal field theories and the theory of conformal blocks, describing
numerical techniques for the bootstrap based on convex optimization, and
summarizing in detail their applications to fixed points in three and four
dimensions with no or minimal supersymmetry.Comment: 81 pages, double column, 58 figures; v3: updated references, minor
typos correcte
Topological aspects of the critical three-state Potts model
We explore the topological defects of the critical three-state Potts spin
system on the torus, Klein bottle and cylinder. A complete characterization is
obtained by breaking down the Fuchs-Runkel-Schweigert construction of 2d
rational CFT to the lattice setting. This is done by applying the strange
correlator prescription to the recently obtained tensor network descriptions of
string-net ground states in terms of bimodule categories [Lootens, Fuchs,
Haegeman, Schweigert, Verstraete, SciPost Phys. 10, 053 (2021)]. The symmetries
are represented by matrix product operators (MPO), as well as intertwiners
between the diagonal tetracritical Ising model and the non-diagonal three-state
Potts model. Our categorical construction lifts the global transfer matrix
symmetries and intertwiners, previously obtained by solving Yang-Baxter
equations, to MPO symmetries and intertwiners that can be locally deformed,
fused and split. This enables the extraction of conformal characters from
partition functions and yields a comprehensive picture of all boundary
conditions.Comment: 71 pages, many figures, includes supplementary materia
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