Abstract We study the Lee–Yang zeros of the quantum ferromagnetic Ising bath via the interaction with the two probe spins. Similarly, as in an earlier paper (Wei and Liu 2012 Phys. Rev. Lett. 109 , 185701), the problem of detecting the zeros is reduced to the exploration of the time evolution of the probe spins. As a result, the relation between the Lee–Yang zeros of the bath and correlation functions of the probe system is obtained. Also, we obtain the relation between the Lee–Yang zeros and values of the entanglement of the probe spins. We apply these results to the 1D Ising spin model with nearest-neighbor interaction, which can be prepared on trapped atoms.
Abstract We study the Lee–Yang zeros of the quantum ferromagnetic Ising bath via the interaction with the two probe spins. Similarly, as in an earlier paper (Wei and Liu 2012 Phys. Rev. Lett. 109 , 185701), the problem of detecting the zeros is reduced to the exploration of the time evolution of the probe spins. As a result, the relation between the Lee–Yang zeros of the bath and correlation functions of the probe system is obtained. Also, we obtain the relation between the Lee–Yang zeros and values of the entanglement of the probe spins. We apply these results to the 1D Ising spin model with nearest-neighbor interaction, which can be prepared on trapped atoms.
Recently in the paper by Peng X. et al. , Phys. Rev. Lett. , 114 (2015) 010601, the experimental observation of the Lee-Yang zeros of an Ising-type spin-(1/2) bath, by measuring the coherence of a probe spin, was reported. We generalize this problem to the case of an arbitrary high-spin bath. Namely, we consider the evolution of a probe arbitrary spin which interacts with a bath composed by N arbitrary spins. As a result, the connection between the observed values of the probe spin, such as magnetization and susceptibility, and the Lee-Yang zeros is found. We apply these results to some models, namely, a triangle spin cluster, the Ising model with a long-range interaction and the 1D Ising model with nearest-neighbor interaction. Also we propose the implementation of these models on real physical systems.
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.
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.
Yang-Lee edge singularities are the branch point of free energy on the complex plane of physical parameters and have been shown to be the simplest universality class of phase transitions.However, Yang-Lee edge singularities have not been regarded as experimentally observable since they occur at complex physical parameters which are unphysical.A recent discovery regarding the relation between partition functions and probe spin coherence makes it experimentally feasible to access the complex plane of physical parameters.However, how to extract the critical point and the critical exponent of Yang-Lee edge singularities in many-body systems, which occurs only at the thermodynamic limit, has still been elusive.Here we show that the quantum coherence of a probe spin coupled to finite-size Ising-type spin systems presents universal scaling behavior near the Yang-Lee edge singularity.The finite-size scaling behavior of the quantum coherence of the probe spin predicts that one can extract the critical point and the critical exponent of the Yang-Lee edge singularity of an Ising-type spin system in the thermodynamic limit from the spin coherence measurement of the probe spin coupled to finite-size Ising-type spin systems.This finding provides a practical approach to studying the nature of Yang-Lee edge singularities of many-body systems.In 1952, Yang and Lee [1, 2] initiated the examination of phase transitions by studying the partition function zeros, termed Lee-Yang zeros, on the complex plane of a magnetic field h (or fugacity z for fluids).They found that for a system above its critical temperature T c , the partition function must be nonzero throughout some neighborhood of the real axis of the magnetic field within a gap determined by two edges at ( ) h T YL .Therefore the free energy is an analytic function of the real magnetic field.On the other hand, below the critical temperature T c , the Lee-Yang zeros will come arbitrarily to the real axis as the thermodynamic limit is taken, destroying the analyticity of the free energy in h for those real fields at which the Lee-Yang zeros accumulate.Kortman and Griffiths [3] pointed out that the edges of Lee-Yang zeros of a many-body system in the thermodynamic limit are singularity points, termed Yang-Lee edge singularities [4].Fisher [4] proposed that the Yang-Lee edge singularity could be considered as a new second order phase transition point with associated critical exponents.Renormalization group analyses [4] show that the Yang-Lee edge singularity is associated with an j i 3 theory and the crossover dimensionality of the Yang-Lee edge singularity is d c = 6.Later, the investigation of the Yang-Lee edge singularity has been extended to many other models, such as the classical nvector model [5], the quantum Heisenberg model [5], the spherical model [6], the quantum one-dimensional (1D) transverse Ising model [7], the hierarchical model [8], branched polymers [9], the directed-site animalsenumeration problem [10], Ising models on fractal lattices [11], Ising systems with correlated disorder [12], fluid models with repulsive-core interactions [13], the antiferromagnetic Ising model [14] etc.A comprehensive review of the study of Yang-Lee edge singularities can be found in [15, 16].Recently, Kibble-Zurek scaling was shown to appear at the Yang-Lee edge singularity [17], which supports that the Yang-Lee edge singularity is similar to conventional second order phase transitions.Yang-Lee edge singularity occurs in the ferromagnetic Ising models above its critical temperatures in a purely imaginary magnetic field h i (figure 1).For > ( ) h h T YL , the partition function acquires zeros, which becomes dense on the line with > ( ) Ih h T YL .The density of Lee-Yang zeros ( ) g T h , in the thermodynamic limit behaves as ~ -s ( ) | ( )| g T h h h T , YL when ( ) h h T YL from above, with σ being the universal critical
We present an experimental scheme to measure the full distribution of many-body observables in spin systems, both in and out of equilibrium, using an auxiliary qubit as a probe. We focus on the determination of the magnetization and the kink number statistics at thermal equilibrium. The corresponding characteristic functions are related to the analytically continued partition function. Thus, both distributions can be directly extracted from experimental measurements of the coherence of a probe qubit that is coupled to an Ising-type bath, as reported in [X. Peng et al., Phys. Rev. Lett. 114, 010601 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.010601] for the detection of Lee-Yang zeros.