It is well known that a Rindler observer measures a nontrivial energy flux, resulting in a thermal description in an otherwise Minkowski vacuum. For systems consisting of large number of degrees of freedom, it is natural to isolate a small subset of them and engineer a steady state configuration in which these degrees of freedom act as Rindler observers. In Holography, this idea has been explored in various contexts, specifically in exploring the strongly coupled dynamics of a fundamental matter sector, in the background of adjoint matters. In this article, we briefly review some features of this physics, ranging from the basic description of such configurations in terms of strings and branes, to observable effects of this effective thermal description.

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Steady States, Thermal Physics, and Holography

Operator growth in open quantum systems: lessons from the dissipative SYK

We discover a new tricritical point realized only in nonequilibrium steady states, using the $\mathrm{AdS}/\mathrm{CFT}$ correspondence. Our system is a ($3+1$)-dimensional strongly coupled large-${N}_{c}$ gauge theory. The tricritical point is associated with a chiral symmetry breaking under the presence of an electric current and a magnetic field. The critical exponents agree with those of the Landau theory of equilibrium phase transitions. This suggests that the presence of a Landau-like phenomenological theory behind our nonequilibrium phase transitions.

Current Driven Tricritical Point in Large- N c Gauge Theory

We study the critical exponents in the universal scaling laws of a holographic nonequilibrium steady state near its critical point of phase transition, which is driven by an ac electric field sitting in the boundary of the bulk. The applied electric field drives the initial superconducting state into a nonequilibrium steady state with vanishing condensate as its amplitude is greater than a critical value. In the vicinity of the nonequilibrium critical point, we numerically calculate the six static and one dynamical critical exponents, and find that they have similar values to those in equilibrium systems within numerical errors.

Universal critical exponents of nonequilibrium phase transitions from holography

It is well-known that a Rindler observer measures a non-trivial energy flux, resulting in a thermal description in an otherwise Minkowski vacuum. For systems consisting of large number of degrees of freedom, it is natural to isolate a small subset of them, and engineer a steady state configuration in which these degrees of freedom act as Rindler observers. In Holography, this idea has been explored in various contexts, specifically in exploring the strongly coupled dynamics of a fundamental matter sector, in the background of adjoint matters. In this article, we briefly review some features of this physics, ranging from the basic description of such configurations in terms of strings and branes, to observable effects of this effective thermal description.

Effective Thermal Physics in Holography: A Brief Review

We study critical phenomena of nonequilibrium phase transitions by using the AdS/CFT correspondence. Our system consists of charged particles interacting with a heat bath of neutral gauge particles. The system is in current-driven nonequilibrium steady state, and the nonequilibrium phase transition is associated with nonlinear electric conductivity. We define a susceptibility as a response of the system to the current variation. We further define a critical exponent from the power-law divergence of the susceptibility. We find that the critical exponent and the critical amplitude ratio of the susceptibility agree with those of the Landau theory of equilibrium phase transitions, if we identify the current as the external field in the Landau theory.

Critical exponents of nonequilibrium phase transitions in AdS /CFT correspondence

We show that a non-Hermitian two coupled Sachdev-Ye-Kitaev (SYK) model can provide thermodynamic structure equivalent to Hermitian two coupled SYK model. The energy spectrum, the entanglement degree of the ground states and the low energy eﬀective action of this model are not inﬂuenced by the non-Hermiticity. The novel biorthogonal ground states demonstrates that two SYK sites, one of which can be in the ground state and the other in the Schwarzian excited state by tuning the non-Hermiticity. We ﬁnd evidence that the free energy is independent of the non-Hermiticity.

Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models

We propose a non-Hermitian two coupled Sachdev-Ye-Kitaev model, but its thermodynamic structure is similar to Hermitian two coupled SYK model. The non-Hermiticity greatly modiﬁes the properties of the ground states and the oﬀ-diagonal Green’s functions. Supersingly, the energy spectrum, the degree of entanglement of the ground states of the two SYK are not inﬂuenced by the non-Hermiticity. Meanwhile, the free energy as a function of temperature shows ﬁrst order phase transition between gapped and gapless phases independent of the non-Hermicity.

A Non-Hermitian two coupled Sachdev-Ye-Kitaev model

We study critical phenomena associated with a spontaneous chiral symmetry breaking in current-driven non-equilibrium steady states by using holography. We ﬁnd that the critical exponents ( γ, ν ) at the tricritical point are asymmetric between the chiral symmetry restored phase and the broken phase. Their values in the broken phase are diﬀerent from those of the mean-ﬁeld theory, whereas other critical exponents are the mean-ﬁeld values. The phase diagram with respect to temperature and current density shows a re-entrant structure: the broken chiral symmetry is restored again at low temperatures in the presence of current density.

Masataka Matsumoto

Papers

Critical exponents of nonequilibrium phase transitions in AdS /CFT correspondence

Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models

A Non-Hermitian two coupled Sachdev-Ye-Kitaev model

Current-induced inverse symmetry breaking and asymmetric critical phenomena at current-driven tricritical point

Tricritical phenomena in holographic chiral phase transitions