49 research outputs found
Fine structures in the spectrum of the open-boundary Heisenberg chain at large anisotropies
At large anisotropies, the spectrum of the Heisenberg XXZ spin chain
separates into `bands' with energies largely determined by the number of domain
walls. The band structure is richer with open boundary conditions: there are
more bands and the bands develop intricate fine structures. We characterize and
explain these structures and substructures in the open-boundary chain. The fine
structures are explained using degenerate perturbation theory. We also present
some dynamical consequences of these sub-band structures, through explicit time
evolution of the wavefunction from initial states motivated by the fine
structure analysis
Persistent entanglement in a class of eigenstates of quantum Heisenberg spin glasses
The eigenstates of a quantum spin glass Hamiltonian with long-range
interaction are examined from the point of view of localisation and
entanglement. In particular, low particle sectors are examined and an anomalous
family of eigenstates is found that is more delocalised but also has larger
inter-spin entanglement. These are then identified as particle-added
eigenstates from the one-particle sector. This motivates the introduction and
the study of random promoted two-particle states, and it is shown that they may
have large delocalisation such as generic ran- dom states and scale exactly
like them. However, the entanglement as measured by two-spin concurrence
displays different scaling with the total number of spins. This shows how for
different classes of complex quantum states entanglement can be qualitatively
different even if localisation measures such as participation ratio are not.Comment: 7 pages, 3 figures, 1 tabl
Avalanches and hysteresis in frustrated superconductors and XY-spin-glasses
We study avalanches along the hysteresis loop of long-range interacting
spin-glasses with continuous XY-symmetry - which serves as a toy model of
granular superconductors with long-range and frustrated Josephson couplings. We
identify sudden jumps in the configurations of the XY-phases, as an
external field is increased. They are initiated by the softest mode of the
inverse susceptibility matrix becoming unstable, which induces an avalanche of
phase updates (or spin alignments). We analyze the statistics of these events,
and study the correlation between the non-linear avalanches and the soft mode
that initiates them. We find that the avalanches follow the directions of a
small fraction of the softest modes of the inverse susceptibility matrix,
similarly as was found in avalanches in jammed systems. In contrast to the
similar Ising spin-glass (Sherrington-Kirkpatrick) studied previously, we find
that avalanches are not distributed with a scale-free power law, but rather
have a typical size which scales with the system size. We also observe that the
Hessians of the spin-glass minima are not part of standard random matrix
ensembles as the lowest eigenvector has a fractal support.Comment: 17 pages, 12 figure
The microscopic origin of thermodynamic entropy in isolated systems
A microscopic understanding of the thermodynamic entropy in quantum systems
has been a mystery ever since the invention of quantum mechanics. In classical
physics, this entropy is believed to be the logarithm of the volume of phase
space accessible to an isolated system [1]. There is no quantum mechanical
analog to this. Instead, Von Neumann's hypothesis for the entropy [2] is most
widely used. However this gives zero for systems with a known wave function,
that is a pure state. This is because it measures the lack of information about
the system rather than the flow of heat as obtained from thermodynamic
experiments. Many arguments attempt to sidestep these issues by considering the
system of interest coupled to a large external one, unlike the classical case
where Boltzmann's approach for isolated systems is far more satisfactory. With
new experimental techniques, probing the quantum nature of thermalization is
now possible [3, 4]. Here, using recent advances in our understanding of
quantum thermalization [5-10] we show how to obtain the entropy as is measured
from thermodynamic experiments, solely from the self-entanglement of the
wavefunction, and find strong numerical evidence that the two are in agreement
for non-integrable systems. It is striking that this entropy, which is closely
related to the concept of heat, and generally thought of as microscopic chaotic
motion, can be determined for systems in energy eigenstates which are
stationary in time and therefore not chaotic, but instead have a very complex
spatial dependence.Comment: Manuscript is 5 pages, 2 figures, plus supplementary materials of 8
pages and 5 figure