Abstract
Quantum phase transitions are a ubiquitous many-body phenomenon that occurs in a wide range of physical systems, including superconductors, quantum spin liquids, and topological materials. However, investigations of quantum critical systems also represent one of the most challenging problems in physics, since highly correlated many-body systems rarely allow for an analytic and tractable description. Here we present a Lee-Yang theory of quantum phase transitions including a method to determine quantum critical points which readily can be implemented within the tensor network formalism and even in realistic experimental setups. We apply our method to a quantum Ising chain and the anisotropic quantum Heisenberg model and show how the critical behavior can be predicted by calculating or measuring the high cumulants of properly defined operators. Our approach provides a powerful formalism to analyze quantum phase transitions using tensor networks, and it paves the way for systematic investigations of quantum criticality in two-dimensional systems.
Highlights
Predicting and understanding the phase behavior of correlated quantum many-body systems constitute one of the most demanding problems in theoretical condensed matter physics and related fields [1,2]
The Lee-Yang formalism has in recent years experienced a surge of interest because of several experiments that have determined the partition function zeros in a variety of physical systems [12,13,14,15] and thereby shown that Lee-Yang zeros are not just a theoretical concept
For h = 1.2 and h = 1.1, the Lee-Yang zeros remain complex in the thermodynamic limit, while for h = 1.0, they reach the real axis at s = 0, signaling a quantum phase transition
Summary
Predicting and understanding the phase behavior of correlated quantum many-body systems constitute one of the most demanding problems in theoretical condensed matter physics and related fields [1,2]. A powerful method that has proven successful in describing thermodynamic phase transitions is the Lee-Yang formalism, which considers the zeros of the partition function in the complex plane of the external control parameters [8,9,10,11]. They provide an efficient tool to predict and understand phase transitions in interacting many-body systems, experimentally [16,17,18,19,20]. Quantum Ising chain and Lee-Yang zeros. (a) The quantum
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