Latest Papers in Condensed Matter Physics

Statistical Mechanics

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Quantum chaos challenges many-body localization (1905.06345v2)

J. Šuntajs, J. Bonča, T. Prosen, L. Vidmar

2019-05-15

Characterizing states of matter through the lens of their ergodic properties is a fascinating new direction of research. In the quantum realm, the many-body localization (MBL) was proposed to be the paradigmatic nonergodic phenomenon, which extends the concept of Anderson localization to interacting systems. At the same time, random matrix theory has established a powerful framework for characterizing the onset of quantum chaos and ergodicity (or the absence thereof) in quantum many-body systems. Here we study a paradigmatic class of models that are expected to exhibit MBL, i.e., disordered spin chains with Heisenberg-like interactions. Surprisingly, we observe that exact calculations show no evidence of approaching MBL while increasing disordered strength in the ergodic regime. Moreover, a scaling analysis suggests that quantum chaotic properties survive for any disorder strength in the thermodynamic limit. Our results are based on calculations of the spectral form factor, which provides a powerful measure for the emergence of many-body quantum chaos.

A general framework to study the extremal phase transition of black holes (1903.03434v2)

Krishnakanta Bhattacharya, Sumit Dey, Bibhas Ranjan Majhi, Saurav Samanta

2019-03-08

We investigate the universality of some features for the extremal phase transition of black holes and unify all the approaches which have been applied in different spacetimes. Unlike the other existing approaches where the information of the spacetime and its dimension is directly used to get various results, we provide a general formulation in which those results are obtained for any arbitrary black hole spacetime having an extremal limit. Calculating the second order moments of fluctuations of some thermodynamic quantities we show that, the phase transition occurs only in the microcanonical ensemble. Without considering any specific black hole we calculate the values of critical exponents for this type of phase transition. These are shown to be in agreement with the values obtained earlier for metric specified cases. Finally we extend our analysis to the geometrothermodynamics (henceforth GTD) formulation. We show that for any black hole, if there is an extremal point, the Ricci scalar for the Ruppeiner metric must diverge at that point.

A deterministic algorithm for counting colorings with colors (1906.01228v2)

Jingcheng Liu, Alistair Sinclair, Piyush Srivastava

2019-06-04

We give a polynomial time deterministic approximation algorithm (an FPTAS) for counting the number of -colorings of a graph of maximum degree , provided only that . This substantially improves on previous deterministic algorithms for this problem, the best of which requires , and matches the natural bound for randomized algorithms obtained by a straightforward application of Markov chain Monte Carlo. In the special case when the graph is also triangle-free, we show that our algorithm applies under the condition , where and are absolute constants. Our result applies more generally to list colorings, and to the partition function of the anti-ferromagnetic Potts model. Our algorithm exploits the so-called "polynomial interpolation" method of Barvinok, identifying a suitable region of the complex plane in which the Potts model partition function has no zeros. Interestingly, our method for identifying this zero-free region leverages probabilistic and combinatorial ideas that have been used in the analysis of Markov chains.

Renormalization-group study of the many-body localization transition in one dimension (1903.02001v3)

Alan Morningstar, David A. Huse

2019-03-05

Using a new approximate strong-randomness renormalization group (RG), we study the many-body localized (MBL) phase and phase transition in one-dimensional quantum systems with short-range interactions and quenched disorder. Our RG is built on those of Zhang [1] and Goremykina [2], which are based on thermal and insulating blocks. Our main addition is to characterize each insulating block with two lengths: a physical length, and an internal decay length for its effective interactions. In this approach, the MBL phase is governed by a RG fixed line that is parametrized by a global decay length , and the rare large thermal inclusions within the MBL phase have a fractal geometry. As the phase transition is approached from within the MBL phase, approaches the finite critical value corresponding to the avalanche instability, and the fractal dimension of large thermal inclusions approaches zero. Our analysis is consistent with a Kosterlitz-Thouless-like RG flow, with no intermediate critical MBL phase.

Onset of synchronization in networks of second-order Kuramoto oscillators with delayed coupling: Exact results and application to phase-locked loops (1906.02643v1)

David Métivier, Lucas Wetzel, Shamik Gupta

2019-06-06

We consider the inertial Kuramoto model of globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we show that the model can be related to a network of phase-locked loops widely used in electronic circuits for generating a stable frequency at multiples of an input frequency. We study the model for a generic choice of the natural frequency distribution of the oscillators, to elucidate how a synchronized phase bifurcates from an incoherent phase as the coupling constant between the oscillators is tuned. We show that in contrast to the case with no delay, here the system in the stationary state may exhibit either a subcritical or a supercritical bifurcation between a synchronized and an incoherent phase, which is dictated by the value of the delay present in the interaction and the precise value of inertia of the oscillators. Our theoretical analysis, performed in the limit , is based on an unstable manifold expansion in the vicinity of the bifurcation, which we apply to the kinetic equation satisfied by the single-oscillator distribution function. We check our results by performing direct numerical integration of the dynamics for large , and highlight the subtleties arising from having a finite number of oscillators.

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