27,283 research outputs found
Fermionic Implementation of Projected Entangled Pair States Algorithm
We present and implement an efficient variational method to simulate
two-dimensional finite size fermionic quantum systems by fermionic projected
entangled pair states. The approach differs from the original one due to the
fact that there is no need for an extra string-bond for contracting the tensor
network. The method is tested on a bi-linear fermionic model on a square
lattice for sizes up to ten by ten where good relative accuracy is achieved.
Qualitatively good results are also obtained for an interacting fermionic
system.Comment: As published in Phys. Rev.
Quantum memories with zero-energy Majorana modes and experimental constraints
In this work we address the problem of realizing a reliable quantum memory
based on zero-energy Majorana modes in the presence of experimental constraints
on the operations aimed at recovering the information. In particular, we
characterize the best recovery operation acting only on the zero-energy
Majorana modes and the memory fidelity that can be therewith achieved. In order
to understand the effect of such restriction, we discuss two examples of noise
models acting on the topological system and compare the amount of information
that can be recovered by accessing either the whole system, or the zero-modes
only, with particular attention to the scaling with the size of the system and
the energy gap. We explicitly discuss the case of a thermal bosonic environment
inducing a parity-preserving Markovian dynamics in which the introduced memory
fidelity decays exponentially in time, independent from system size, thus
showing the impossibility to retrieve the information by acting on the
zero-modes only. We argue, however, that even in the presence of experimental
limitations, the Hamiltonian gap is still beneficial to the storage of
information.Comment: 18 pages, 7 figures. Updated to published versio
Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians
The Jordan--Wigner transformation plays an important role in spin models.
However, the non-locality of the transformation implies that a periodic chain
of spins is not mapped to a periodic or an anti-periodic chain of lattice
fermions. Since only the bond is different, the effect is negligible for
large systems, while it is significant for small systems. In this paper, it is
interesting to find that a class of periodic spin chains can be exactly mapped
to a periodic chain and an anti-periodic chain of lattice fermions without
redundancy when the Jordan--Wigner transformation is implemented. For these
systems, possible high degeneracy is found to appear in not only the ground
state but also the excitation states. Further, we take the one-dimensional
compass model and a new XY-XY model () as
examples to demonstrate our proposition. Except for the well-known
one-dimensional compass model, we will see that in the XY-XY model, the
degeneracy also grows exponentially with the number of sites.Comment: 9 pages, 3 figure
Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
Motivated by the prospect of attaining Majorana modes at the ends of
nanowires, we analyze interacting Majorana systems on general networks and
lattices in an arbitrary number of dimensions, and derive various universal
spin duals. Such general complex Majorana architectures (other than those of
simple square or other crystalline arrangements) might be of empirical
relevance. As these systems display low-dimensional symmetries, they are
candidates for realizing topological quantum order. We prove that (a) these
Majorana systems, (b) quantum Ising gauge theories, and (c) transverse-field
Ising models with annealed bimodal disorder are all dual to one another on
general graphs. As any Dirac fermion (including electronic) operator can be
expressed as a linear combination of two Majorana fermion operators, our
results further lead to dualities between interacting Dirac fermionic systems.
The spin duals allow us to predict the feasibility of various standard
transitions as well as spin-glass type behavior in {\it interacting} Majorana
fermion or electronic systems. Several new systems that can be simulated by
arrays of Majorana wires are further introduced and investigated: (1) the {\it
XXZ honeycomb compass} model (intermediate between the classical Ising model on
the honeycomb lattice and Kitaev's honeycomb model), (2) a checkerboard lattice
realization of the model of Xu and Moore for superconducting arrays,
and a (3) compass type two-flavor Hubbard model with both pairing and hopping
terms. By the use of dualities, we show that all of these systems lie in the 3D
Ising universality class. We discuss how the existence of topological orders
and bounds on autocorrelation times can be inferred by the use of symmetries
and also propose to engineer {\it quantum simulators} out of these Majorana
networks.Comment: v3,19 pages, 18 figures, submitted to Physical Review B. 11 new
figures, new section on simulating the Hubbard model with nanowire systems,
and two new appendice
Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
We examine in details the connections between topological and entanglement
properties of short-range resonating valence bond (RVB) wave functions using
Projected Entangled Pair States (PEPS) on kagome and square lattices on
(quasi-)infinite cylinders with generalized boundary conditions (and perimeters
with up to 20 lattice spacings). Making use of disconnected topological sectors
in the space of dimer lattice coverings, we explicitly derive (orthogonal)
"minimally entangled" PEPS RVB states. For the kagome lattice, we obtain, using
the quantum Heisenberg antiferromagnet as a reference model, the finite size
scaling of the energy separations between these states. In particular, we
extract two separate (vanishing) energy scales corresponding (i) to insert a
vison line between the two ends of the cylinder and (ii) to pull out and freeze
a spin at either end. We also investigate the relations between bulk and
boundary properties and show that, for a bipartition of the cylinder, the
boundary Hamiltonian defined on the edge can be written as a product of a
highly non-local projector with an emergent (local) su(2)-invariant
one-dimensional (superfluid) t--J Hamiltonian, which arises due to the symmetry
properties of the auxiliary spins at the edge. This multiplicative structure, a
consequence of the disconnected topological sectors in the space of dimer
lattice coverings, is characteristic of the topological nature of the states.
For minimally entangled RVB states, it is shown that the entanglement spectrum,
which reflects the properties of the edge modes, is a subset (half for kagome
RVB) of the spectrum of the local Hamiltonian, providing e.g. a simple argument
on the origin of the topological entanglement entropy S0=-ln 2 of Z2 spin
liquids. We propose to use these features to probe topological phases in
microscopic Hamiltonians and some results are compared to existing DMRG data.Comment: 15 pages, 19 figures. Large extension of the paper. Finite size
scaling of the (topological) ground state energy splittings added (for the
Kagome quantum antiferromagnet
The geometric order of stripes and Luttinger liquids
It is argued that the electron stripes as found in correlated oxides have to
do with an unrecognized form of order. The manifestation of this order is the
robust property that the charge stripes are at the same time anti-phase
boundaries in the spin system. We demonstrate that the quantity which is
ordering is sublattice parity, referring to the geometric property of a
bipartite lattice that it can be subdivided in two sublattices in two different
ways. Re-interpreting standard results of one dimensional physics, we
demonstrate that the same order is responsible for the phenomenon of
spin-charge separation in strongly interacting one dimensional electron
systems. In fact, the stripe phases can be seen from this perspective as the
precise generalization of the Luttinger liquid to higher dimensions. Most of
this paper is devoted to a detailed exposition of the mean-field theory of
sublattice parity order in 2+1 dimensions. Although the quantum-dynamics of the
spin- and charge degrees of freedom is fully taken into account, a perfect
sublattice parity order is imposed. Due to novel order-out-of-disorder physics,
the sublattice parity order gives rise to full stripe order at long wavelength.
This adds further credibility to the notion that stripes find their origin in
the microscopic quantum fluctuations and it suggests a novel viewpoint on the
relationship between stripes and high Tc superconductivity.Comment: 29 pages, 14 figures, 1 tabl
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