One of the most fundamental problems in quantum many-body physics is the characterization of correlations among thermal states. Of particular relevance is the thermal area law, which justifies the tensor network approximations to thermal states with a bond dimension growing polynomially with the system size. In the regime of sufficiently low temperatures, which is particularly important for practical applications, the existing techniques do not yield optimal bounds. Here, we propose a new thermal area law that holds for generic many-body systems on lattices. We improve the temperature dependence from the original O(β) to O~(β2/3), thereby suggesting diffusive propagation of entanglement by imaginary time evolution. This qualitatively differs from the real-time evolution which usually induces linear growth of entanglement. We also prove analogous bounds for the Rényi entanglement of purification and the entanglement of formation. Our analysis is based on a polynomial approximation to the exponential function which provides a relationship between the imaginary-time evolution and random walks. Moreover, for one-dimensional (1D) systems with n spins, we prove that the Gibbs state is well-approximated by a matrix product operator with a sublinear bond dimension of eO~(βlog(n))√. This allows us to rigorously establish, for the first time, a quasi-linear time classical algorithm for constructing an MPS representation of 1D quantum Gibbs states at arbitrary temperatures of β=o(log(n)). Our new technical ingredient is a block decomposition of the Gibbs state, that bears resemblance to the decomposition of real-time evolution given by Haah et al., FOCS'18.
Oriana Diessel completed her doctorate in Richard Schmidt's independent research group. Her theoretical work focusses on two special features of many-body systems: so-called "polarons" and previously unknown phase transitions in light-matter systems. In her work, Oriana Diessel developed models to theoretically describe the two phenomena, thereby providing a further building block for our understanding of quantum many-body theory.
Being elected as a member of the National Academy of Sciences is regarded as one of the most distinguished honours a scientist can receive. While the majority of members hold U.S. citizenship, up to 30 international members are elected annually. NAS members are “charged with providing independent, objective advice on matters related to science and technology”.
Theorists in the research group of Mari Carmen Bañuls at MPQ have come one step closer to understanding the evolution of quantum many body systems over time. In their work, recently published in the specialized journal Physical Review Letters, they formulated an algorithm to simulate the dynamics of quantum systems consisting of many particles out of equilibrium – a notoriously difficult task.
Dr Bañuls, group leader in the Theory Department at MPQ, has earned special recognition in her many years of excellent research of complex quantum systems, and is now starting her own W2 research group. Her research focuses on the development and application of tensor network methods for the numerical simulation of quantum many-body systems and quantum dynamic phenomena beyond equilibrium.
His work on the principles and applications of quantum physics, such as in quantum information theory or the simulation of complex many-body systems, as well as his overall scientific achievements would contribute to revolutionising the world as we know it today, explained the university. It is the ninth honorary doctorate that Ignacio Cirac has been awarded to date.