# Latest Research Papers In Condensed Matter Physics | (Cond-Mat.Stat-Mech) 2019-06-14

**Latest Papers in Condensed Matter Physics**

Statistical Mechanics

### Out-of-time-order correlators at infinite temperature: Scrambling, Order and Topological Phase Transitions (1906.05241v1)

**Ceren B. Dağ, L. -M. Duan, Kai Sun**

*2019-06-12*

We report a numerical observation where the infinite-temperature out-of-time-order correlators (OTOCs) directly probe quantum phase transitions at zero temperature. This is in direct contrast to common intuition where quantum effects are washed away by strong thermal fluctuations at high temperature. We compare numerical results with exact analytic solutions and find that the effect is not a coincidence. Instead, it is generic and highly robust as long as the underlying system can be mapped to a 1D Majorana chain. Using the Majorana basis, we find that this is a topological phenomenon, where infinite-temperature OTOCs probe zero temperature topological phases via the detection of the topological degeneracy in the entire spectrum. This insight leads to a new family of interacting and nonintegrable systems whose dynamics do not show scrambling. Our results reveal an interesting interplay between topological order and information scrambling, suggesting new ways to utilize the scrambling of quantum many-body systems.

### Electromagnetism at finite temperature: a density operator approach (1906.05219v1)

**Daigo Oue**

*2019-06-12*

In order to analyse classical electromagnetism in a medium at finite temperature, we introduce "optical density operator," and reformulate Maxwell equations with the operator, starting from the Dirac-equation-like formulation of electromagnetism. The thermal state of electromagnetic field in the medium can be calculated from the "optical Dirac Hamiltonian," which is the effective Hamiltonian in the Dirac-like formulation. In the thermal state, the two transverse modes (left-handed and right-handed circularly polarisation) of electromagnetic fields exist at the same ratio. According to the asymptotics of the thermal state, at the low temperature limit, there is correlation between the electric field and the magnetic field. This means that there exists an electromagnetic wave at the thermal equilibrium, and this recovers Maxwell classical electromagnetism. In contrast, the correlation vanishes at the high temperature limit. This means that electromagnetic waves are unsustainable but just independent electric fields and magnetic fields at the high temperature limit.

### Entropic elasticity and negative thermal expansion in a simple cubic crystal (1906.05213v1)

**David Wendt, Emil Bozin, Joerg Neuefeind, Katharine Page, Wei Ku, Limin Wang, Brent Fultz, Alexei Tkachenko, Igor Zaliznyak**

*2019-06-12*

While most solids expand when heated, some materials show the opposite behavior: negative thermal expansion (NTE). In polymers and biomolecules, NTE originates from the entropic elasticity of an ideal, freely-jointed chain. The origin of NTE in solids has been widely believed to be different. Our neutron scattering study of a simple cubic NTE material, ScF3, overturns this consensus. We observe that the correlation in the positions of the neighboring fluorine atoms rapidly fades on warming, indicating an uncorrelated thermal motion constrained by the rigid Sc-F bonds. This leads us to a quantitative theory of NTE in terms of entropic elasticity of a floppy network crystal, which is in remarkable agreement with experimental results. We thus reveal the formidable universality of the NTE phenomenon in soft and hard matter.

### Is Deep Learning an RG Flow? (1906.05212v1)

**Ellen de Mello Koch, Robert de Mello Koch, Ling Cheng**

*2019-06-12*

Although there has been a rapid development of practical applications, theoretical explanations of deep learning are in their infancy. A possible starting point suggests that deep learning performs a sophisticated coarse graining. Coarse graining is the foundation of the renormalization group (RG), which provides a systematic construction of the theory of large scales starting from an underlying microscopic theory. In this way RG can be interpreted as providing a mechanism to explain the emergence of large scale structure, which is directly relevant to deep learning. We pursue the possibility that RG may provide a useful framework within which to pursue a theoretical explanation of deep learning. A statistical mechanics model for a magnet, the Ising model, is used to train an unsupervised RBM. The patterns generated by the trained RBM are compared to the configurations generated through a RG treatment of the Ising model. We argue that correlation functions between hidden and visible neurons are capable of diagnosing RG-like coarse graining. Numerical experiments show the presence of RG-like patterns in correlators computed using the trained RBMs. The observables we consider are also able to exhibit important differences between RG and deep learning.

### An Efficient Simulation Method for Determining the Density of States of Complex Systems (1901.01430v2)

**Takuya Hayashi, Yuko Okamoto**

*2019-01-05*

By combining two generalized-ensemble algorithms, the Multicanonical Replica-Exchange Method and the Replica-Exchange Wang-Landau method, we have developed an effective simulation method to determine the density of states of large and complex systems. In order to verify the effectiveness of our algorithm, we performed simulations of a square-lattice Ising model by several methods. The results showed that the density of states obtained by the present method is more accurate than that is estimated by the two methods used separately.

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