64 research outputs found
Exact results for fidelity susceptibility of the quantum Ising model: The interplay between parity, system size, and magnetic field
We derive an exact closed-form expression for fidelity susceptibility of
even- and odd-sized quantum Ising chains in the transverse field. To this aim,
we diagonalize the Ising Hamiltonian and study the gap between its positive and
negative parity subspaces. We derive an exact closed-form expression for the
gap and use it to identify the parity of the ground state. We point out
misunderstanding in some of the former studies of fidelity susceptibility and
discuss its consequences. Last but not least, we rigorously analyze the
properties of the gap. For example, we derive analytical expressions showing
its exponential dependence on the ratio between the system size and the
correlation length.Comment: 11 pages, updated references, version accepted in JP
Breaking the entanglement barrier: Tensor network simulation of quantum transport
The recognition that large classes of quantum many-body systems have limited
entanglement in the ground and low-lying excited states led to dramatic
advances in their numerical simulation via so-called tensor networks. However,
global dynamics elevates many particles into excited states, and can lead to
macroscopic entanglement and the failure of tensor networks. Here, we show that
for quantum transport -- one of the most important cases of this failure -- the
fundamental issue is the canonical basis in which the scenario is cast: When
particles flow through an interface, they scatter, generating a "bit" of
entanglement between spatial regions with each event. The frequency basis
naturally captures that -- in the long-time limit and in the absence of
inelastic scattering -- particles tend to flow from a state with one frequency
to a state of identical frequency. Recognizing this natural structure yields a
striking -- potentially exponential in some cases -- increase in simulation
efficiency, greatly extending the attainable spatial- and time-scales, and
broadening the scope of tensor network simulation to hitherto inaccessible
classes of non-equilibrium many-body problems.Comment: Published version; 6+9 pages; 4+4 figures; Added: an example of
interacting reservoirs, further evidence on performance scaling, and extended
discussion of the numerical detail
Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model
We propose a symmetric version of the multi-scale entanglement
renormalization Ansatz (MERA) in two spatial dimensions (2D) and use this
Ansatz to find an unknown ground state of a 2D quantum system. Results in the
simple 2D quantum Ising model on the square lattice are found to be
very accurate even with the smallest non-trivial truncation parameter.Comment: version to appear in Phys. Rev. Letter
Symmetry breaking bias and the dynamics of a quantum phase transition
The Kibble-Zurek mechanism predicts the formation of topological defects and
other excitations that quantify how much a quantum system driven across a
quantum critical point fails to be adiabatic. We point out that, thanks to the
divergent linear susceptibility at the critical point, even a tiny symmetry
breaking bias can restore the adiabaticity. The minimal required bias scales
like , where are the
critical exponents and is a quench time. We test this prediction by
DMRG simulations of the quantum Ising chain. It is directly applicable to the
recent emulation of quantum phase transition dynamics in the Ising chain with
ultracold Rydberg atoms.Comment: 5+1 pages, 5+1 figures; close to published versio
Anomalous behavior of the energy gap in the one-dimensional quantum XY model
We re-examine the well-studied one dimensional spin-1/2 model to reveal
its nontrivial energy spectrum, in particular the energy gap between the ground
state and the first excited state. In the case of the isotropic model --
the model -- the gap behaves very irregularly as a function of the system
size at a second order transition point. This is in stark contrast to the usual
power-law decay of the gap and is reminiscent of the similar behavior at the
first order phase transition in the infinite-range quantum model. The gap
also shows nontrivial oscillatory behavior for the phase transitions in the
anisotropic model in the incommensurate phase. We observe a close relation
between this anomalous behavior of the gap and the correlation functions. These
results, those for the isotropic case in particular, are important from the
viewpoint of quantum annealing where the efficiency of computation is strongly
affected by the size dependence of the energy gap.Comment: 25 pages, 8 figures. arXiv admin note: substantial text overlap with
arXiv:1501.0292
Matrix product state renormalization
The truncation or compression of the spectrum of Schmidt values is inherent
to the matrix product state (MPS) approximation of one-dimensional quantum
ground states. We provide a renormalization group picture by interpreting this
compression as an application of Wilson's numerical renormalization group along
the imaginary time direction appearing in the path integral representation of
the state. The location of the physical index is considered as an impurity in
the transfer matrix and static MPS correlation functions are reinterpreted as
dynamical impurity correlations. Coarse-graining the transfer matrix is
performed using a hybrid variational ansatz based on matrix product operators,
combining ideas of MPS and the multi-scale entanglement renormalization ansatz.
Through numerical comparison with conventional MPS algorithms, we explicitly
verify the impurity interpretation of MPS compression, as put forward by [V.
Zauner et al., New J. Phys. 17, 053002 (2015)] for the transverse-field Ising
model. Additionally, we motivate the conceptual usefulness of endowing MPS with
an internal layered structure by studying restricted variational subspaces to
describe elementary excitations on top of the ground state, which serves to
elucidate a transparent renormalization group structure ingrained in MPS
descriptions of ground states.Comment: 15 pages, 10 figures, published versio
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