1,971 research outputs found
Entanglement Entropy of U(1) Quantum Spin Liquids
We here investigate the entanglement structure of the ground state of a
(3+1)-dimensional U(1) quantum spin liquid, which is described by the
deconfined phase of a compact U(1) gauge theory. A gapless photon is the only
low-energy excitation, with matter existing as deconfined but gapped
excitations of the system. It is found that, for a given bipartition of the
system, the elements of the entanglement spectrum can be grouped according to
the electric flux between the two regions, leading to a useful interpretation
of the entanglement spectrum in terms of electric charges living on the
boundary. The entanglement spectrum is also given additional structure due to
the presence of the gapless photon. Making use of the Bisognano-Wichmann
theorem and a local thermal approximation, these two contributions to the
entanglement (particle and photon) are recast in terms of boundary and bulk
contributions, respectively. Both pieces of the entanglement structure give
rise to universal subleading terms (relative to the area law) in the
entanglement entropy, which are logarithmic in the system size (log L), as
opposed to the subleading constant term in gapped topologically ordered
systems. The photon subleading logarithm arises from the low-energy conformal
field theory and is essentially local in character. The particle subleading
logarithm arises due to the constraint of closed electric loops in the
wavefunction and is shown to be the natural generalization of topological
entanglement entropy to the U(1) spin liquid. This contribution to the
entanglement entropy can be isolated by means of the Grover-Turner-Vishwanath
construction (which generalizes the Kitaev-Preskill scheme to three
dimensions).Comment: 15+6 page
The quantum phases of matter
I present a selective survey of the phases of quantum matter with varieties
of many-particle quantum entanglement. I classify the phases as gapped,
conformal, or compressible quantum matter. Gapped quantum matter is illustrated
by a simple discussion of the Z_2 spin liquid, and connections are made to
topological field theories. I discuss how conformal matter is realized at
quantum critical points of realistic lattice models, and make connections to a
number of experimental systems. Recent progress in our understanding of
compressible quantum phases which are not Fermi liquids is summarized. Finally,
I discuss how the strongly-coupled phases of quantum matter may be described by
gauge-gravity duality. The structure of the large N limit of SU(N) gauge
theory, coupled to adjoint fermion matter at non-zero density, suggests aspects
of gravitational duals of compressible quantum matter.Comment: 35 pages, 21 figures; Rapporteur presentation at the 25th Solvay
Conference on Physics, "The Theory of the Quantum World", Brussels, Oct 2011;
(v2+v3+v4) expanded holographic discussion and referencin
Entanglement and Second Quantization in the Framework of the Fermionic Projector
A method is developed for realizing entanglement and general second quantized
fermionic and bosonic fields in the framework of the fermionic projector.Comment: 41 pages, LaTeX, 2 figures, shortened (published version,
supplemented by appendix
Lieb-Robinson and the butterfly effect
As experiments are increasingly able to probe the quantum dynamics of systems
with many degrees of freedom, it is interesting to probe fundamental bounds on
the dynamics of quantum information. We elaborate on the relationship between
one such bound---the Lieb-Robinson bound---and the butterfly effect in
strongly-coupled quantum systems. The butterfly effect implies the ballistic
growth of local operators in time, which can be quantified with the "butterfly"
velocity . Similarly, the Lieb-Robinson velocity places a state
independent ballistic upper bound on the size of time evolved operators in
non-relativistic lattice models. Here, we argue that is a state-dependent
effective Lieb-Robinson velocity. We study the butterfly velocity in a wide
variety of quantum field theories using holography and compare with free
particle computations to understand the role of strong coupling. We find that,
depending on the way length and time scale, acquires a temperature
dependence and decreases towards the IR. We also comment on experimental
prospects and on the relationship between the butterfly velocity and signaling.Comment: 5+5 pages, 0 figures. v2: updated references and additional
clarification
- …