1,135 research outputs found
Obtaining highly-excited eigenstates of many-body localized Hamiltonians by the density matrix renormalization group
The eigenstates of many-body localized (MBL) Hamiltonians exhibit low
entanglement. We adapt the highly successful density-matrix renormalization
group method, which is usually used to find modestly entangled ground states of
local Hamiltonians, to find individual highly excited eigenstates of many body
localized Hamiltonians. The adaptation builds on the distinctive spatial
structure of such eigenstates. We benchmark our method against the well studied
random field Heisenberg model in one dimension. At moderate to large disorder,
we find that the method successfully obtains excited eigenstates with high
accuracy, thereby enabling a study of MBL systems at much larger system sizes
than those accessible to exact-diagonalization methods.Comment: Published version. Slightly expanded discussion; supplement adde
Strongly correlated fermions on a kagome lattice
We study a model of strongly correlated spinless fermions on a kagome lattice
at 1/3 filling, with interactions described by an extended Hubbard Hamiltonian.
An effective Hamiltonian in the desired strong correlation regime is derived,
from which the spectral functions are calculated by means of exact
diagonalization techniques. We present our numerical results with a view to
discussion of possible signatures of confinement/deconfinement of fractional
charges.Comment: 10 pages, 10 figure
Correlated Fermions on a Checkerboard Lattice
A model of strongly correlated spinless fermions hopping on a checkerboard
lattice is mapped onto a quantum fully-packed loop model. We identify a large
number of fluctuationless states specific to the fermionic case. We also show
that for a class of fluctuating states, the fermionic sign problem can be
gauged away. This claim is supported by numerically evaluating the energies of
the low-lying states. Furthermore, we analyze in detail the excitations at the
Rokhsar-Kivelson point of this model thereby using the relation to the height
model and the single-mode approximation.Comment: 4 Pages, 3 Figures; v4: updated version published in Phys. Rev.
Lett.; one reference adde
Dynamics after a sweep through a quantum critical point
The coherent quantum evolution of a one-dimensional many-particle system
after sweeping the Hamiltonian through a critical point is studied using a
generalized quantum Ising model containing both integrable and non-integrable
regimes. It is known from previous work that universal power laws appear in
such quantities as the mean number of excitations created by the sweep. Several
other phenomena are found that are not reflected by such averages: there are
two scaling regimes of the entanglement entropy and a relaxation that is
power-law rather than exponential. The final state of evolution after the
quench is not well characterized by any effective temperature, and the
Loschmidt echo converges algebraically to a constant for long times, with
cusplike singularities in the integrable case that are dynamically broadened by
nonintegrable perturbations.Comment: 4 pages, 4 figure
Real-time dynamics in the one-dimensional Hubbard model
We consider single-particle properties in the one-dimensional repulsive
Hubbard model at commensurate fillings in the metallic phase. We determine the
real-time evolution of the retarded Green's function by matrix-product state
methods. We find that at sufficiently late times the numerical results are in
good agreement with predictions of nonlinear Luttinger liquid theory. We argue
that combining the two methods provides a way of determining the
single-particle spectral function with very high frequency resolution.Comment: 10 pages, 6 figures. Minor edits from v1. Version as publishe
Detection of Symmetry Protected Topological Phases in 1D
A topological phase is a phase of matter which cannot be characterized by a
local order parameter. It has been shown that gapped phases in 1D systems can
be completely characterized using tools related to projective representations
of the symmetry groups. We show how to determine the matrices of these
representations in a simple way in order to distinguish between different
phases directly. From these matrices we also point out how to derive several
different types of non-local order parameters for time reversal, inversion
symmetry and symmetry, as well as some more general cases
(some of which have been obtained before by other methods). Using these
concepts, the ordinary string order for the Haldane phase can be related to a
selection rule that changes at the critical point. We furthermore point out an
example of a more complicated internal symmetry for which the ordinary string
order cannot be applied.Comment: 12 pages, 9 Figure
On confined fractional charges: a simple model
We address the question whether features known from quantum chromodynamics
(QCD) can possibly also show up in solid-state physics. It is shown that
spinless fermions of charge on a checkerboard lattice with nearest-neighbor
repulsion provide for a simple model of confined fractional charges. After
defining a proper vacuum the system supports excitations with charges
attached to the ends of strings. There is a constant confining force acting
between the fractional charges. It results from a reduction of vacuum
fluctuations and a polarization of the vacuum in the vicinity of the connecting
strings.Comment: 5 pages, 3 figure
Entanglement Transitions in Unitary Circuit Games
Repeated projective measurements in unitary circuits can lead to an
entanglement phase transition as the measurement rate is tuned. In this work,
we consider a different setting in which the projective measurements are
replaced by dynamically chosen unitary gates that minimize the entanglement.
This can be seen as a one-dimensional unitary circuit game in which two players
get to place unitary gates on randomly assigned bonds at different rates: The
"entangler" applies a random local unitary gate with the aim of generating
extensive (volume law) entanglement. The "disentangler," based on limited
knowledge about the state, chooses a unitary gate to reduce the entanglement
entropy on the assigned bond with the goal of limiting to only finite (area
law) entanglement. In order to elucidate the resulting entanglement dynamics,
we consider three different scenarios: (i) a classical discrete height model,
(ii) a Clifford circuit, and (iii) a general unitary circuit. We find
that both the classical and Clifford circuit models exhibit phase transitions
as a function of the rate that the disentangler places a gate, which have
similar properties that can be understood through a connection to the
stochastic Fredkin chain. In contrast, the "entangler" always wins when using
Haar random unitary gates and we observe extensive, volume law entanglement for
all non-zero rates of entangling.Comment: 18 pages, 12 figure
- …