889 research outputs found
Detecting subsystem symmetry protected topological order via entanglement entropy
Subsystem symmetry protected topological (SSPT) order is a type of quantum
order that is protected by symmetries acting on lower-dimensional subsystems of
the entire system. In this paper, we show how SSPT order can be characterized
and detected by a constant correction to the entanglement area law, similar to
the topological entanglement entropy. Focusing on the paradigmatic
two-dimensional cluster phase as an example, we use tensor network methods to
give an analytic argument that almost all states in the phase exhibit the same
correction to the area law, such that this correction may be used to reliably
detect the SSPT order of the cluster phase. Based on this idea, we formulate a
numerical method that uses tensor networks to extract this correction from
ground-state wave functions. We use this method to study the fate of the SSPT
order of the cluster state under various external fields and interactions, and
find that the correction persists unless a phase transition is crossed, or the
subsystem symmetry is explicitly broken. Surprisingly, these results uncover
that the SSPT order of the cluster state persists beyond the cluster phase,
thanks to a new type of subsystem time-reversal symmetry. Finally, we discuss
the correction to the area law found in three-dimensional cluster states on
different lattices, indicating rich behavior for general subsystem symmetriesComment: 17 pages. v2: Published version, minor changes throughou
Projected entangled-pair states can describe chiral topological states
We show that Projected Entangled-Pair States (PEPS) in two spatial dimensions
can describe chiral topological states by explicitly constructing a family of
such states with a non-trivial Chern number. They are ground states of two
different kinds of free-fermion Hamiltonians: (i) local and gapless; (ii)
gapped, but with hopping amplitudes that decay according to a power law. We
derive general conditions on topological free fermionic PEPS which show that
they cannot correspond to exact ground states of gapped, local parent
Hamiltonians, and provide numerical evidence demonstrating that they can
nevertheless approximate well the physical properties of topological insulators
with local Hamiltonians at arbitrary temperatures.Comment: v2: minor changes, references added. v3: accepted version,
Journal-Ref adde
Computational Difficulty of Computing the Density of States
We study the computational difficulty of computing the ground state
degeneracy and the density of states for local Hamiltonians. We show that the
difficulty of both problems is exactly captured by a class which we call #BQP,
which is the counting version of the quantum complexity class QMA. We show that
#BQP is not harder than its classical counting counterpart #P, which in turn
implies that computing the ground state degeneracy or the density of states for
classical Hamiltonians is just as hard as it is for quantum Hamiltonians.Comment: v2: Accepted version. 9 pages, 1 figur
Nonlocal resources in the presence of Superselection Rules
Superselection rules severely alter the possible operations that can be
implemented on a distributed quantum system. Whereas the restriction to local
operations imposed by a bipartite setting gives rise to the notion of
entanglement as a nonlocal resource, the superselection rule associated with
particle number conservation leads to a new resource, the \emph{superselection
induced variance} of local particle number. We show that, in the case of pure
quantum states, one can quantify the nonlocal properties by only two additive
measures, and that all states with the same measures can be asymptotically
interconverted into each other by local operations and classical communication.
Furthermore we discuss how superselection rules affect the concepts of
majorization, teleportation and mixed state entanglement.Comment: 4 page
Quantum entanglement theory in the presence of superselection rules
Superselection rules severly constrain the operations which can be
implemented on a distributed quantum system. While the restriction to local
operations and classical communication gives rise to entanglement as a nonlocal
resource, particle number conservation additionally confines the possible
operations and should give rise to a new resource. In [Phys. Rev. Lett. 92,
087904 (2004), quant-ph/0310124] we showed that this resource can be quantified
by a single additional number, the superselection induced variance (SiV)
without changing the concept of entanglement. In this paper, we give the
results on pure states in greater detail; additionally, we provide a discussion
of mixed state nonlocality with superselection rules where we consider both
formation and distillation. Finally, we demonstrate that SiV is indeed a
resource, i.e., that it captures how well a state can be used to overcome the
restrictions imposed by the superselection rule.Comment: 16 pages, 5 figure
Dielectronic Resonance Method for Measuring Isotope Shifts
Longstanding problems in the comparison of very accurate hyperfine-shift
measurements to theory were partly overcome by precise measurements on
few-electron highly-charged ions. Still the agreement between theory and
experiment is unsatisfactory. In this paper, we present a radically new way of
precisely measuring hyperfine shifts, and demonstrate its effectiveness in the
case of the hyperfine shift of and in
. It is based on the precise detection of dielectronic
resonances that occur in electron-ion recombination at very low energy. This
allows us to determine the hyperfine constant to around 0.6 meV accuracy which
is on the order of 10%
Inaccessible entanglement in symmetry protected topological phases
We study the entanglement structure of symmetry-protected topological (SPT)
phases from an operational point of view by considering entanglement
distillation in the presence of symmetries. We demonstrate that non-trivial SPT
phases in one-dimension necessarily contain some entanglement which is
inaccessible if the symmetry is enforced. More precisely, we consider the
setting of local operations and classical communication (LOCC) where the local
operations commute with a global onsite symmetry group , which we call
-LOCC, and we define the inaccessible entanglement as the
entanglement that cannot be used for distillation under -LOCC. We derive a
tight bound on which demonstrates a direct relation between
inaccessible entanglement and the SPT phase, namely , where is the topologically protected edge
mode degeneracy of the SPT phase with symmetry . For particular
phases such as the Haldane phase, so the bound becomes
an equality. We numerically investigate the distribution of states throughout
the bound, and show that typically the region near the upper bound is highly
populated, and also determine the nature of those states lying on the upper and
lower bounds. We then discuss the relation of to string order
parameters, and also the extent to which it can be used to distinguish
different SPT phases of matter.Comment: 16 pages, 7 figure
Symmetries and boundary theories for chiral Projected Entangled Pair States
We investigate the topological character of lattice chiral Gaussian fermionic
states in two dimensions possessing the simplest descriptions in terms of
projected entangled-pair states (PEPS). They are ground states of two different
kinds of Hamiltonians. The first one, , is local,
frustration-free, and gapless. It can be interpreted as describing a quantum
phase transition between different topological phases. The second one,
is gapped, and has hopping terms scaling as
with the distance . The gap is robust against local perturbations, which
allows us to define a Chern number for the PEPS. As for (non-chiral)
topological PEPS, the non-trivial topological properties can be traced down to
the existence of a symmetry in the virtual modes that are used to build the
state. Based on that symmetry, we construct string-like operators acting on the
virtual modes that can be continuously deformed without changing the state. On
the torus, the symmetry implies that the ground state space of the local parent
Hamiltonian is two-fold degenerate. By adding a string wrapping around the
torus one can change one of the ground states into the other. We use the
special properties of PEPS to build the boundary theory and show how the
symmetry results in the appearance of chiral modes, and a universal correction
to the area law for the zero R\'{e}nyi entropy.Comment: 29 pages, 14 figure
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