23 research outputs found
Fermions in Geodesic Witten Diagrams
We develop the embedding formalism for odd dimensional Dirac spinors in AdS
and apply it to the (geodesic) Witten diagrams including fermionic degrees of
freedom. We first show that the geodesic Witten diagram (GWD) with fermion
exchange is equivalent to the conformal partial waves associated with the spin
one-half primary field. Then, we explicitly demonstrate the GWD decomposition
of the Witten diagram including the fermion exchange with the aid of the split
representation. The geodesic representation of CPW indeed gives the useful
basis for computing the Witten diagrams.Comment: 12 pages + appendices; v2: some comments and appendices added,
published versio
Entanglement Entropy for 2D Gauge Theories with Matters
We investigate the entanglement entropy in 1+1-dimensional gauge
theories with various matter fields using the lattice regularization. Here we
use extended Hilbert space definition for entanglement entropy, which contains
three contributions; (1) classical Shannon entropy associated with
superselection sector distribution, where sectors are labelled by irreducible
representations of boundary penetrating fluxes, (2) logarithm of the dimensions
of their representations, which is associated with "color entanglement", and
(3) EPR Bell pairs, which give "genuine" entanglement. We explicitly show that
entanglement entropies (1) and (2) above indeed appear for various multiple
"meson" states in gauge theories with matter fields. Furthermore, we employ
transfer matrix formalism for gauge theory with fundamental matter field and
analyze its ground state using hopping parameter expansion (HPE), where the
hopping parameter is roughly the inverse square of the mass for the matter.
We evaluate the entanglement entropy for the ground state and show that all
(1), (2), (3) above appear in the HPE, though the Bell pair part (3) appears in
higher order than (1) and (2) do. With these results, we discuss how the ground
state entanglement entropy in the continuum limit can be understood from the
lattice ground state obtained in the HPE.Comment: 73 pages, 7 figure
Inhomogeneous quenches as state preparation in two-dimensional conformal field theories
The non-equilibrium process where the system does not evolve to the
featureless state is one of the new central objects in the non-equilibrium
phenomena. In this paper, starting from the short-range entangled state in the
two-dimensional conformal field theories (d CFTs), the boundary state with a
regularization, we evolve the system with the inhomogeneous Hamiltonians called
M\"obius/SSD ones. Regardless of the details of CFTs considered in this paper,
during the M\"obius evolution, the entanglement entropy exhibits the periodic
motion called quantum revival. During SSD time evolution, except for some
subsystems, in the large time regime, entanglement entropy and mutual
information are approximated by those for the vacuum state. We argue the time
regime for the subsystem to cool down to vacuum one is , where , , and are time, system, and
subsystem sizes. This finding suggests the inhomogeneous quench induced by the
SSD Hamiltonian may be used as the preparation for the approximately-vacuum
state. We propose the gravity dual of the systems considered in this paper,
furthermore, and generalize it. In addition to them, we discuss the relation
between the inhomogenous quenches and continuous multi-scale entanglement
renormalization ansatz (cMERA).Comment: 32+4 pages, 11 figure
Efficient Simulation of Low Temperature Physics in One-Dimensional Gapless Systems
We discuss the computational efficiency of the finite temperature simulation
with the minimally entangled typical thermal states (METTS). To argue that
METTS can be efficiently represented as matrix product states, we present an
analytic upper bound for the average entanglement Renyi entropy of METTS for
Renyi index . In particular, for 1D gapless systems described by
CFTs, the upper bound scales as where is
the central charge and is the system size. Furthermore, we numerically find
that the average Renyi entropy exhibits a universal behavior characterized by
the central charge and is roughly given by half of the analytic upper bound.
Based on these results, we show that METTS provide a significant speedup
compared to employing the purification method to analyze thermal equilibrium
states at low temperatures in 1D gapless systems.Comment: 6 pages, revte