Beyond Universality: Protocol-Dependent Critical Exponents

Arinjoy De, Patrick D. Cook, Mostafa Ali +8 more

Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-spin resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents, depending on the quench protocol. While a generic quench can lead to thermal critical behavior, we find that a second quench from one critical state to another (i.e. a double quench) results in a new universal non-equilibrium behavior, identified by a set of critical exponents distinct from their equilibrium counterparts. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond equilibrium.

Leo P. Kadanoff

Yu-Rong Shu, Shuai Yin

The concept of universality class lies at the core of phase transition physics, with each class uniquely characterized by a dedicated set of critical exponents. Here, we introduce the concept of initial-state-dictated dynamical universality classes in nonequilibrium quantum critical dynamics. By studying the imaginary-time relaxation dynamics of the dimerized Heisenberg model, we demonstrate that distinct kinds of initial states can give rise to different dynamical universality classes within the same equilibrium universality class. Specifically, we find that "classical'' paramagnetic (random-spin) and "quantum'' paramagnetic (dimerized and antidimerized) initial states yield drastically different critical initial slip exponents in the bulk. This initial-state dependence also extends to boundary critical dynamics, where different initial states yield different surface critical initial slip exponents even within the same boundary universality class. Remarkably, for the antidimerized initial state, we uncover an anomalous scaling law violating the conventional relation between the bulk and surface critical initial slip exponents. Our results establish an initial-state-controlled dynamical classification of quantum criticality that extends beyond the conventional equilibrium universality paradigm.

M.J. Holwerda, W.L.G.A.M. van Neerven, R. P. Van Royen

Hendrik Ballhausen

A derivative expansion of the effective average action beyond first order yields renormalization group functional flow equations which are used for the computation of critical exponents of the Ising universality class. The critical exponent nu in D=3 is consistent with high-precision methods.