Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods

Abstract

The distribution of Yang-Lee zeros in the ferromagnetic Ising model in both two and three dimensions is studied on the complex field plane directly in the thermodynamic limit via the tensor network methods. The partition function is represented as a contraction of a tensor network and is efficiently evaluated with an iterative tensor renormalization scheme. The free-energy density and the magnetization are computed on the complex field plane. Via the discontinuity of the magnetization, the density of the Yang-Lee zeros is obtained to lie on the unit circle, consistent with the Lee-Yang circle theorem. Distinct features are observed at different temperatures-below, above and at the critical temperature. Application of the tensor-network approach is also made to the q-state Potts models in both two and three dimensions and a previous debate on whether, in the thermodynamic limit, the Yang-Lee zeros lie on a unit circle for q > 2 is resolved: they clearly do not lie on a unit circle except at the zero temperature. For the Potts models (q = 3, 4, 5, 6) investigated in two dimensions, as the temperature is lowered the radius of the zeros at a fixed angle from the real axis shrinks exponentially towards unity with the inverse temperature.

Lee-Yang theory of the Curie-Weiss model and its rare fluctuations

“…For the Curie-Weiss model, all spins interact however far apart, and as a result, the large-deviation function becomes bimodal below the critical temperature. We expect that for spin lattices with short-range interactions, for example, the Ising model [56][57][58][59], the large-deviation function will be upper convex also below the critical temperature.…”

Ising chain with topological degeneracy induced by dissipation

“…As far as we know, although non-Hermitian systems indeed have some peculiar features and some of them have been proved that can be equivalent to Hermitian systems in some particular conditions [24][25][26][27][28][29], the complex field is always seen as unphysical. Recently some works, including theoretical and experimental research on Lee Yang zeros, which are the points on the complex plane of physical parameters, are proposed [30][31][32][33][34][35][36]. It relates a complex field to the real world in some extent.…”

“…(30) on finite N chains obtained by exact diagonalization. Panels (a1)-(c1) and (a2)-(c2) are energy gap E2 − E1 and overlap O ± (R) defined in Eq (34),. respectively.…”

Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model

“…They could thereby explain the nonanalytic behavior of the free energy that develops in the thermodynamic limit and signals a phase transition. The Lee-Yang formalism has been applied to a variety of equilibrium problems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], and it has been realized that the framework can also be used to understand nonequilibrium phase transitions [19][20][21][22][23][24], such as dynamical phase transitions in quantum systems after a quench [25][26][27] and space-time phase transitions in glass formers [28][29][30][31] and open quantum systems [32][33][34].…”

“…2469-9950/2020/102(17)/174418 (12) 174418-1 ©2020 American Physical Society general properties of partition functions, including an important connection between the zeros of the partition function and its logarithmic derivatives, which deliver the cumulants of interest [9,32,44,45]. The idea is illustrated in Fig.…”