Physics

The area law for entanglement provides one of the most important connections between information theory and quantum many-body physics. It is not only related to the universality of quantum phases, but also to efficient numerical simulations in the ground state (i.e., the lowest energy state).  Various numerical observations have led to a strong belief that the area law is true for every non-critical phase in short-range interacting systems [1]. The so-called area-law conjecture states that the entanglement entropy is proportional to the surface region of subsystem if the ground state is non-critical (or gapped). 

However, the area law for long-range interacting systems is still elusive as the long-range interaction results in correlation patterns similar to the ones in critical phases. Here, we show that for generic non-critical one-dimensional ground states, the area law robustly holds without any corrections even under long-range interactions [2]. Our result guarantees an efficient description of ground states by the matrix-product state in experimentally relevant long-range systems, which justifies the density-matrix renormalization algorithm. In the present talk, I will give an overview of the results, and show ideas of the proof if the time allows. 

[1] J. Eisert, M. Cramer, and M. B. Plenio, ``Colloquium: Area laws for the entanglement entropy,'' Rev. Mod. Phys. 82, 277–306 (2010).

[2] T. Kuwahara and K. Saito, ``Area law of non-critical ground states in 1d long-range interacting systems,'' arXiv preprint arXiv:1908.11547 (2019),

As our understanding of the universe and its fundamental building blocks extends to shorter and shorter distances, experiments capable of probing these scales are becoming increasingly difficult to construct. Fundamental particle physics faces a potential crisis: an absence of data at the shortest possible scales. Yet remarkably, even in the absence of experimental data, the requirement of theoretical consistency puts stringent constraints on viable models of fundamental particles and their interactions. In this talk I’ll discuss a variety of criteria that constrain theories of particles in flat spacetime and de Sitter. Such criteria have the possibility to address questions such as: What low energy theories admit consistent UV completions? Which massive particles are allowed in an interacting theory? Is string theory the unique weakly coupled UV completion of General Relativity?

Stochastic thermodynamics is a recently established discipline of statistical physics.It explores fundamental aspects of non-equilibrium processes by applying and extending concepts from equilibrium thermodynamics to the non-equilibrium realm, typically on thelevel of single particle trajectories monitored over the entire system evolution. This approach provides an adequate framework to investigate the behaviour of ``small systems’’ on mesoscopic scales for which thermal fluctuations may have a significant or even dominant effect on the general system properties.We consider such small systems consisting of so-called Brownian particles (like colloids in suspension or biological macromolecules in a cell). After introducing the standard model for Brownian motion, we briefly describe the ideas and concepts leading to a (trajectory-wise) thermodynamic characterization of Brownian motion, and finally elaborateon central results from stochastic thermodynamics. As a refinement of the second law of thermodynamics, the most famous amongst these results are probably the fluctuation theorems.