Far-from-Equilibrium Field Theory of Many-Body Quantum Spin Systems: Prethermalization and Relaxation of Spin Spiral States in Three Dimensions

October 14, 2015

Figure 2: The spin-2PI formalism illustrated*
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What happens when an isolated quantum system is set in motion from an initial nonequilibrium state that possesses certain orders? In classical thermodynamics, this problem is exemplified by the irreversible expansion of a gas in an isolated chamber after suddenly doubling the chamber size. Generically, one expects to observe a gradual relaxation to a thermal equilibrium state as the details of the initial state are progressively washed away in collisions. In certain cases, however, the formation of strong quantum correlations between the particles can conspire to slow down the relaxation process, resulting in a multistage dissolution of the initial information via long detours to intermediate states. In technical terms, these intermediate states are referred to as prethermal states, which are distinct from thermal equilibrium. Even though prethermalization is believed to be a rather ubiquitous phenomenon, so far it has only been experimentally observed in weakly interacting, one-dimensional systems. Unfortunately, currently available theoretical methods for describing the quantum dynamics of experimentally realizable models of strongly correlated systems in higher dimensions are inadequate.

In the latest issue of Physics Review X, Caltec postdoc (and Harvard Physics grad) Mehrtash Babadi, Prof. Eugene Demler, and Harvard Physics Associate Michael Knap present a new formalism using methods of quantum field theory to study the real-time dynamics of interacting quantum spins*.

The physicists focus on relaxation dynamics in the three-dimensional quantum Heisenberg model of spin-1/2 systems, one of the paradigmatic models of strong quantum correlations. Inspired by recent experiments using ultracold atoms in a quantum gas microscope, they study the evolution of spins initially prepared in helical spiral states. They find that spiral states that energetically allow spontaneous symmetry breaking upon thermalization also exhibit a pronounced two-step relaxation with long-lived prethermal states, and other states relax in a simple monotonic fashion. Curiously, the hierarchical relaxation we find here bears a strong resemblance to aging dynamics in classical glassy systems. They also show that instabilities in the system exhibit self-regulation.

Understanding the emergence of slow degrees of freedom near thermodynamic phase transitions has implications far beyond condensed matter physics and is, for example, important for the description of the early Universe. The authors expect that their work will contribute to establishing new connections among condensed matter, soft matter, cosmology, and atomic physics.

*see M. Babadi, E. Demler, and M. Knap, "Far-from-Equilibrium Field Theory of Many-Body Quantum Spin Systems: Prethermalization and Relaxation of Spin Spiral States in Three Dimensions," Phys. Rev. X 5, 041005 (12 October 2015) doi: http://dx.doi.org/10.1103/PhysRevX.5.041005