Experimental Observation of Equilibrium and Dynamical Quantum Phase Transitions via Out-of-Time-Ordered Correlators.

The out-of-time-ordered correlators (OTOC), a fundamental concept for quantifying quantum information scrambling, has recently been suggested to be an order parameter to dynamically detect both equilibrium quantum phase transitions (EQPTs) and dynamical quantum phase transitions (DQPTs). Here we report the first experimental observation of EQPTs and DQPTs in a quantum spin chain via quench dynamics of OTOC on a nuclear magnetic resonance quantum simulator. We observe that the quench dynamics of the OTOC can unambiguously detect the DQPTs and the equilibrium critical point, while conventional order parameters such as the longitudinal magnetization can not. Moreover, we investigate the two-body correlations throughout the quench dynamics, and find that OTOC can extract the equilibrium critical point with higher accuracy and is more robust to decoherence than that of two-body correlation. Our experiment paves a way for experimentally investigating DQPTs through OTOCs and for studying the EQPTs through the nonequilibrium quantum quench dynamics with quantum simulators.

Relations between heat exchange and Rényi divergences.

In this work, we establish an exact relation which connects the heat exchange between two systems initialized in their thermodynamic equilibrium states at different temperatures and the Rényi divergences between the initial thermodynamic equilibrium state and the final nonequilibrium state of the total system. The relation tells us that the various moments of the heat statistics are determined by the Renyi divergences between the initial equilibrium state and the final nonequilibrium state of the global system. In particular the average heat exchange is quantified by the relative entropy between the initial equilibrium state and the final nonequilibrium state of the global system. The relation is applicable to both finite classical systems and finite quantum systems.

Probing Conformal Invariant of Non-unitary Two-Dimensional Systems by Central Spin Decoherence.

Universality classes of non-unitary critical theories in two-dimensions are characterized by the central charge. However, experimental determination of the central charge of a non-unitary critical theory has not been done before because of the intrinsic difficulty that complex parameters usually occur in non-unitary theory, which is not physical. Here we propose to extract the effective central charge of the non-unitary critical point of a two-dimensional lattice model from the quantum coherence measurement of a probe spin which is coupled to the lattice model. A recent discovery shows that quantum coherence of a probe spin which is coupled to a bath is proportional to the partition function of the bath with a complex parameter. Thus the effective central charge of a non-unitary conformal field theory may be extracted from quantum coherence measurement of a probe spin which is coupled to a bath. We have applied the method to the Yang-Lee edge singularity of the two-dimensional Ising model and extracted the effective central charge of the Yang-Lee edge singularity with good precision and tested other predictions of non-unitary conformal field theory. This work paves the way for the first experimental observation of the effective central charge of non-unitary conformal field theory.

Quantum work relations and response theory in parity-time-symmetric quantum systems.

In this work, we show that a universal quantum work relation for a quantum system driven arbitrarily far from equilibrium extends to a parity-time- (PT-) symmetric quantum system with unbroken PT symmetry, which is a consequence of microscopic reversibility. The quantum Jarzynski equality, linear response theory, and Onsager reciprocal relations for the PT-symmetric quantum system are recovered as special cases of the universal quantum work relation in a PT-symmetric quantum system. In the regime of broken PT symmetry, the universal quantum work relation does not hold because the norm is not preserved during the dynamics.

Universal Critical Behaviours in Non-Hermitian Phase Transitions.

Quantum phase transitions occur in non-Hermitian systems. In this work we show that density functional theory, for the first time, uncovers universal critical behaviors for quantum phase transitions and quantum entanglement in non-Hermitian many-body systems. To be specific, we first prove that the non-degenerate steady state of a non-Hermitian quantum many body system is a universal function of the first derivative of the steady state energy with respect to the control parameter. This finding has far-reaching consequences for non-Hermitian systems. First, it bridges the non-analytic behavior of physical observable and no-analytic behavior of steady state energy, which explains why the quantum phase transitions in non-Hermitian systems occur for finite systems. Second, it predicts universal scaling behaviors of any physical observable at non-Hermitian phase transition point with scaling exponent being (1 - 1/p) with p being the number of coalesced states at the exceptional point. Third, it reveals that quantum entanglement in non-Hermitian phase transition point presents universal scaling behaviors with critical exponents being (1 - 1/p). These results uncover universal critical behaviors in non-Hermitian phase transitions and provide profound connections between entanglement and phase transition in non-Hermitian quantum many-body physics.

Anomalous dissipation and kinetic-energy distribution in pipes at very high Reynolds numbers.

A symmetry-based theory is developed for the description of (streamwise) kinetic energy K in turbulent pipes at extremely high Reynolds numbers (Re's). The theory assumes a mesolayer with continual deformation of wall-attached eddies which introduce an anomalous dissipation, breaking the exact balance between production and dissipation. An outer peak of K is predicted above a critical Re of 10^{4}, in good agreement with experimental data. The theory offers an alternative explanation for the recently discovered logarithmic distribution of K. The concept of anomalous dissipation is further supported by a significant modification of the k-ω equation, yielding an accurate prediction of the entire K profile.

Thermodynamic holography.

The holographic principle states that the information about a volume of a system is encoded on the boundary surface of the volume. Holography appears in many branches of physics, such as optics, electromagnetism, many-body physics, quantum gravity, and string theory. Here we show that holography is also an underlying principle in thermodynamics, a most important foundation of physics. The thermodynamics of a system is fully determined by its partition function. We prove that the partition function of a finite but arbitrarily large system is an analytic function on the complex plane of physical parameters, and therefore the partition function in a region on the complex plane is uniquely determined by its values along the boundary. The thermodynamic holography has applications in studying thermodynamics of nano-scale systems (such as molecule engines, nano-generators and macromolecules) and provides a new approach to many-body physics.

Experimental observation of Lee-Yang zeros.

Lee-Yang zeros are points on the complex plane of physical parameters where the partition function of a system vanishes and hence the free energy diverges. Lee-Yang zeros are ubiquitous in many-body systems and fully characterize their thermodynamics. Notwithstanding their fundamental importance, Lee-Yang zeros have never been observed in experiments, due to the intrinsic difficulty that they would occur only at complex values of physical parameters, which are generally regarded as unphysical. Here we report the first observation of Lee-Yang zeros, by measuring quantum coherence of a probe spin coupled to an Ising-type spin bath. The quantum evolution of the probe spin introduces a complex phase factor and therefore effectively realizes an imaginary magnetic field. From the measured Lee-Yang zeros, we reconstructed the free energy of the spin bath and determined its phase transition temperature. This experiment opens up new opportunities of studying thermodynamics in the complex plane.

Phase transitions in the complex plane of physical parameters.

At low temperature, a thermodynamic system undergoes a phase transition when a physical parameter passes through a singularity point of the free energy. This corresponds to the formation of a new order. At high temperature, thermal fluctuations destroy the order. Correspondingly, the free energy is a smooth function of the physical parameter and singularities only occur at complex values of the parameter. Since a complex valued parameter is unphysical, no phase transitions are expected when the physical parameter is varied. Here we show that the quantum evolution of a system, initially in thermal equilibrium and driven by a designed interaction, is equivalent to the partition function of a complex parameter. Therefore, we can access the complex singularity points of thermodynamic functions and observe phase transitions even at high temperature. We further show that such phase transitions in the complex plane are related to topological properties of the renormalization group flows of the complex parameters. This result makes it possible to study thermodynamics in the complex plane of physical parameters.

Lee-Yang zeros and critical times in decoherence of a probe spin coupled to a bath.

Phase transitions are not usually seen in the time domain. Here, we report on the finding of critical times at which a physical observable, in the thermodynamic limit, becomes nonanalytic as a function of time. We find that the coherence of a probe spin coupled to a many-body system vanishes at times in one-to-one correspondence to the Lee-Yang zeros of the partition function of the many-body system. In the thermodynamic limit, the Lee-Yang zeros form a continuum cut in the complex plane of fugacity and the probe spin coherence presents sudden death and birth at the critical times corresponding to the Yang-Lee singularities. These results provide new experimental possibilities in many-body physics.