arXiv subjects

Auditya Sharma

Publications and source records attributed to Auditya Sharma.

At least 55 records · Page 3Linked to original sources

arXiv2019

`Muhammad Ali effect' and incoherent destruction of Wannier-Stark localization in a stochastic field

We calculate an exact expression for the probability propagator for a noisy electric field driven tight-binding lattice. The noise considered is a two-level jump process or a telegraph process (TP) which jumps randomly between two values $\pmμ$. In the absence of a static field and in the limit of zero jump rate of the noisy field we find that the dynamics yield Bloch oscillations with frequency $μ$, while with an additional static field $ε$ we find oscillatory motion with a superposition of frequencies $(ε\pm μ)$. On the other hand, when the jump rate is `rapid', and in the absence of a static field, the stochastic field averages to zero if the two states of the TP are equally probable `a-priori'. In that case, we see a delocalization effect. The intimate relationship between the rapid relaxation case and the zero field case is a manifestation of what we call the `Muhammad Ali effect'. It is interesting to note that even for zero static field and rapid relaxation, Bloch oscillations ensue if there is a bias $δp$ in the probabilities of the two levels. Remarkably, the Wannier-Stark localization caused by an additional static field is destroyed if the latter is tuned to be exactly equal and opposite to the average stochastic field $μδp$. This is an example of \emph{incoherent} destruction of Wannier-Stark localization.

cond-mat.dis-nn↗

arXiv2018

Biased random walks with finite mean first passage time

A power-law distance-dependent biased random walk model with a tuning parameter ($σ$) is introduced in which finite mean first passage times are realizable if $σ$ is less than a critical value $σ_c$. We perform numerical simulations in $1$-dimension to obtain $σ_c \sim 1.14$. The three-dimensional version of this model is related to the phenomenon of chemotaxis. Diffusiophoretic theory supplemented with coarse-grained simulations establish the connection with the specific value of $σ= 2$ as a consequence of in-built solvent diffusion. A variant of the one-dimensional power-law model is found to be applicable in the context of a stock investor devising a strategy for extricating their portfolio out of loss.

cond-mat.stat-mech↗

arXiv2018

Characteristic length scales from entanglement dynamics in electric-field-driven tight-binding chains

We study entanglement dynamics in the nearest-neighbour fermionic chain that is subjected to both DC and AC electric fields. The dynamics gives the well known Bloch oscillations in the DC field case provided that the system size is larger than the Bloch length whereas in the AC field case the entropy is bounded and oscillates with the driving frequency at the points of dynamical localization, and has a logarithmic growth at other points. A combined AC + DC field yields super Bloch oscillations for the system size larger than the super Bloch length which puts a constraint on the device size in a typical non-equilibrium set-up to observe super Bloch oscillations where the device is connected to the leads. Entanglement entropy provides useful signatures for all of these phenomena, and an alternate way to capture the various length scales involved.

cond-mat.mes-hall↗

arXiv2018

Self-organized critical behavior and marginality in Ising spin glasses

We have studied numerically the states reached in a quench from various temperatures in the one-dimensional fully-connected Kotliar, Anderson and Stein Ising spin glass model. This is a model where there are long-range interactions between the spins which falls off a\ s a power $σ$ of their separation. We have made a detailed study in particular of the energies of the states reached in a quench from infinite temperature and their overlaps, including the spin glass susceptibility. In the regime where $σ\le 1/2$, where th\ e model is similar to the Sherrington-Kirkpatrick model, we find that the spin glass susceptibility diverges logarithmically with increasing $N$, the number of spins in the system, whereas for $σ> 1/2$ it remains finite. We attribute the behavior for $σ\le 1/\ 2$ to \emph {self-organized critical behavior}, where the system after the quench is close to the transition between states which have trivial overlaps and those with the non-trivial overlaps associated with replica symmetry breaking. We have also found by studying the d\ istribution of local fields that the states reached in the quench have marginal stability but only when $σ\le 1/2$.

cond-mat.stat-mech↗

arXiv2018

Landauer current and mutual information in a bosonic quantum dot

We study the quantum transport of bosons through a quantum dot coupled to two macroscopic heat baths $L$ and $R$, held at fixed temperatures $T_{L}$ and $T_{R}$ respectively. We manage to cast the particle as well as the heat current into the Landauer form. Following the correlation matrix approach, we compute the time-dependent mutual information of the dot with the baths. We find that mutual information goes logarithmically as the number of bosons, and at low temperatures, it is possible to set up the parameters in such a way that in steady-state, the mutual information goes quadratically as a function of current.

cond-mat.mes-hall↗

arXiv2018

Many-body entanglement in a topological chiral ladder

We find that the topological phase transition in a chiral ladder is characterized by dramatic signatures in many body entanglement entropy between the legs, close to half-filling. The value of entanglement entropy for various fillings close to half-filling is identical, at the critical point, but splays out on either side, thus showing a sharp signature at the transition point. A second signature is provided by the change in entanglement entropy when a particle is added (or subtracted) from half-filling which turns out to be exactly $-\log{2}$ in the trivial phase, but zero in the topological phase. A microscopic understanding of tendencies to form singlets along the rungs in the trivial phase, and along the diagonals in the topological phase, is afforded by a study of concurrence. At the topological phase transition the magnitude of the derivative of the average concurrence of all the rungs shows a sharp peak. Also, at the critical point, the average concurrence is the same for various fillings close to half-filling, but splays out on either side, just like entanglement entropy.

cond-mat.mes-hall↗

arXiv2018

Entanglement contour perspective for strong area law violation in a disordered long-range hopping model

We numerically investigate the link between the delocalization-localization transition and entanglement in a disordered long-range hopping model of spinless fermions by studying various static and dynamical quantities. This includes the inverse participation ratio, level-statistics, entanglement entropy and number fluctuations in the subsystem along with quench and wave-packet dynamics. Finite systems show delocalized, quasi-localized and localized phases. The delocalized phase shows strong area-law violation whereas the (quasi)localized phase adheres to (for large subsystems) the strict area law. The idea of `entanglement contour' nicely explains the violation of area-law and its relationship with `fluctuation contour' reveals a signature at the transition point. The relationship between entanglement entropy and number fluctuations in the subsystem also carries signatures for the transition in the model. Results from Aubry-Andre-Harper model are compared in this context. The propagation of charge and entanglement are contrasted by studying quench and wavepacket dynamics at the single-particle and many-particle levels.

cond-mat.str-el↗

arXiv2017

Phase diagram for the Harper model of the honeycomb lattice

The Harper equation arising out of a tight-binding model of electrons on a honeycomb lattice subject to a uniform magnetic field perpendicular to the plane is studied. Contrasting and complementary approaches involving von Neumann entropy, fidelity, fidelity susceptibility, multifractal analysis are employed to characterize the phase diagram. The phase diagram consists of three phases: two metallic phases and an insulating phase. A variant model where next nearest neighbor hopping is included, exhibits a mobility edge and does not allow for a simple single phase diagram characterizing all the eigenstates.

cond-mat.str-el↗

arXiv2017

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.

quant-ph↗

arXiv2016

The metastable minima of the Heisenberg spin glass in a random magnetic field

We have studied zero temperature metastable states in classical $m$-vector component spin glasses in the presence of $m$-component random fields (of strength $h_{r}$) for a variety of models, including the Sherrington Kirkpatrick (SK) model, the Viana Bray (VB) model and the randomly diluted one-dimensional models with long-range power law interactions. For the SK model we have calculated analytically its complexity (the log of the number of minima) for both the annealed case and the quenched case, both for fields above and below the de Almeida Thouless (AT) field ($h_{AT} > 0$ for $m>2$). We have done quenches starting from a random initial state by putting spins parallel to their local fields until convergence and found that in zero field it always produces minima which have zero overlap with each other. For the $m=2$ and $m=3$ cases in the SK model the final energy reached in the quench is very close to the energy $E_c$ at which the overlap of the states would acquire replica symmetry breaking features. These minima have marginal stability and will have long-range correlations between them. In the SK limit we have analytically studied the density of states $ρ(λ)$ of the Hessian matrix in the annealed approximation. Despite the absence of continuous symmetries, the spectrum extends down to zero with the usual $\sqrtλ$ form for the density of states for $h_{r} h_{AT}$, there is a gap in the spectrum which closes up as $h_{AT}$ is approached. For the VB model and the other models our numerical work shows that there always exist some low-lying eigenvalues and there never seems to be a gap. There is no sign of the AT transition in the quenched states reached from infinite temperature for any model but the SK model, which is the only model which has zero complexity above $h_{AT}$.

cond-mat.dis-nn↗

arXiv2015

Susceptibilities for the Müller-Hartmann-Zitartz countable infinity of phase transitions on a Cayley tree

We obtain explicit susceptibilities for the countable infinity of phase transition temperatures of Müller-Hartmann-Zitartz on a Cayley tree. The susceptibilities are a product of the zeroth spin with the sum of an appropriate set of averages of spins on the outermost layer of the tree. A clear physical understanding for these strange phase transitions emerges naturally. In the thermodynamic limit, the susceptibilities tend to zero above the transition and to infinity below it.

cond-mat.stat-mech↗

arXiv2015

Landauer Current and Mutual Information

We study quantum evolution of the entanglement of a quantum dot connected to left and right leads initially maintained at chemical potentials $μ_{L}$ and $μ_{R}$ respectively, within the non-interacting resonant-level model. The full nonequilirbium mixed state density matrix of the whole system is written down exactly, and entanglement is computed by recourse to the notion of mutual information. A strong and direct correlation is found between the Landauer current, and the entanglement at all times, the steady-state values in particular displaying a quadratic relationship at high temperatures. Strikingly, it is found that one can obtain a maximally entangled quantum dot by simply applying a sufficiently large `source-drain' voltage $V_{SD}$ even at high temperatures.

cond-mat.str-el↗

arXiv2015

Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices

We show how the area law for the entanglement entropy may be violated by free fermions on a lattice and look for conditions leading to the emergence of a volume law. We give an explicit construction of the states with maximal entanglement entropy based on the fact that, once a bipartition of the lattice in two complementary sets $A$ and $\bar{A}$ is given, the states with maximal entanglement entropy (volume law) may be factored into Bell-pairs (BP) formed by two states with support on $A$ and $\bar{A}$. We then exhibit, for translational invariant fermionic systems on a lattice, an Hamiltonian whose ground state is such to yield an exact volume law. As expected, the corresponding Fermi surface has a fractal topology. We also provide some examples of fermionic models for which the ground state may have an entanglement entropy $S_A$ between the area and the volume law, building an explicit example of a one-dimensional free fermion model where $S_A (L) \propto L^β$ with $β$ being intermediate between $β= 0$ (area law) and $β= 1$ (BP-state inducing volume law). For this model, the dispersion relation has a "zig-zag" structure leading to a fractal Fermi surface whose counting box dimension equals, for large lattices, $β$. Our analysis clearly relates the violation of the area law for the entanglement entropy of the ground state to the emergence of a non-trivial topology of the Fermi surface.

cond-mat.stat-mech↗

arXiv2015

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 $T=0$ 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.

cond-mat.dis-nn↗

arXiv2013

Using memory to identify phase transitions on a Cayley Tree

We provide a concrete and systematic connection between the statistical physics of the Ising ferromagnet on a Cayley tree, and the study of memory in exponentially expanding spaces. Memory turns out to be a clear signal of the `Bethe-Peierls' phase transition, and the average of memory divided by its standard deviation provides a clear signal of the `spin-glass' transition temperature. Numerical Monte Carlo simulations are used to make transparent the existence of the two different transition temperatures. The quantities used to spot the phase transitions with Monte Carlo could be useful when studying other systems where analytical methods don't work.

cond-mat.stat-mech↗

arXiv2013

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.

cond-mat.str-el↗

arXiv2012

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.

quant-ph↗

arXiv2011

Study of the de Almeida-Thouless line using one-dimensional power-law diluted Heisenberg Spin Glasses

We test for the presence or absence of the de Almeida-Thouless line using one-dimensional power-law diluted Heisenberg spin glass model, in which the rms strength of the interactions decays with distance, r as 1/r^{sigma}. It is argued that varying the power sigma is analogous to varying the space dimension d in a short-range model. For sigma=0.6, which is in the mean field regime regime, we find clear evidence for an AT line. For sigma = 0.85, which is in the non-mean-field regime and corresponds to a space dimension of close to 3, we find no AT line, though we cannot rule one out for very small fields. Finally for sigma=0.75, which is in the non-mean-field regime but closer to the mean-field boundary, the evidence suggests that there is an AT line, though the possibility that even larger sizes are needed to see the asymptotic behavior can not be ruled out.

cond-mat.dis-nn↗