Abstract Entanglement plays a key role in quantum physics, but how much information it can extract from many-body systems is still an open question, particularly regarding quantum criticalities and emergent symmetries. In this work, we systematically study the entanglement entropy (EE) and derivative entanglement entropy (DEE) near quantum phase transitions in various quantum many-body systems. A one-parameter scaling relation between the DEE and system size at the critical point has been derived for the first time, which successfully obtains the critical exponent via data collapse. Furthermore, we find that the EE peaks at the (emergent) symmetry-enhanced first-order transition, reflecting higher symmetry breaking. This work provides a new paradigm for quantum many-body research from the perspective of EE and DEE.
Abstract Entanglement plays a key role in quantum physics, but how much information it can extract from many-body systems is still an open question, particularly regarding quantum criticalities and emergent symmetries. In this work, we systematically study the entanglement entropy (EE) and derivative entanglement entropy (DEE) near quantum phase transitions in various quantum many-body systems. A one-parameter scaling relation between the DEE and system size at the critical point has been derived for the first time, which successfully obtains the critical exponent via data collapse. Furthermore, we find that the EE peaks at the (emergent) symmetry-enhanced first-order transition, reflecting higher symmetry breaking. This work provides a new paradigm for quantum many-body research from the perspective of EE and DEE.
Critical phenomena, characterized by abrupt changes in macroscopic properties near phase transition points, exhibit universal scaling behavior independent of microscopic details. This paper explores the hypothesis that entropy serves as a fundamental universal scaling law governing these phenomena. We review the theoretical foundations of critical phenomena, including Landau theory and the renormalization group, highlighting the role of critical exponents and scaling functions. We then propose a framework where the configurational entropy, entanglement entropy, and other entropic measures exhibit universal scaling, linking them directly to the underlying critical exponents. Our methodology involves analyzing how entropy behaves under coarse-graining transformations near critical points, identifying a potential entropic fixed point in the renormalization group flow. We present theoretical arguments suggesting that the information content, as quantified by various entropy definitions, reflects the diverging correlation length and the emergent scale invariance at criticality. The discussion extends to how different entropic forms, such as Rényi and Tsallis entropies, might provide a more generalized framework for understanding critical behavior in complex and non-extensive systems. By demonstrating entropy's role as a universal scaling law, this work offers a unifying perspective on critical phenomena, deepening our understanding of phase transitions and the emergence of macroscopic order from microscopic fluctuations.
Motivated by recent development of the concept of the disorder operator and its relation with entanglement entropy in bosonic systems, here we show the disorder operator successfully probes many aspects of quantum entanglement in fermionic many-body systems. From both analytical and numerical computations in free and interacting fermion systems in 1D and 2D, we find the disorder operator and the entanglement entropy exhibit similar universal scaling behavior, as a function of the boundary length of the subsystem, but with subtle yet important differences. In 1D they both follow the \log{L} log L scaling behavior with the coefficient determined by the Luttinger parameter for disorder operator, and the conformal central charge for entanglement entropy. In 2D they both show the universal L\log L L log L scaling behavior in free and interacting Fermi liquid states, with the coefficients depending on the geometry of the Fermi surfaces. However at a 2D quantum critical point with non-Fermi-liquid state, extra symmetry information is needed in the design of the disorder operator, so as to reveal the critical fluctuations as does the entanglement entropy. Our results demonstrate the fermion disorder operator can be used to probe quantum many-body entanglement related to global symmetry, and provide new tools to explore the still largely unknown territory of highly entangled fermion quantum matter in 2 or higher dimensions.
The entanglement exhibits extremal or singular behavior near quantum critical points (QCPs) in many condensed matter models. These intriguing phenomena, however, still call for a widely accepted understanding. In this paper we study this issue in holographic framework. We investigate the connection between the holographic entanglement entropy (HEE) and the quantum phase transition (QPT) in a lattice-deformed Einstein-Maxwell-Dilaton theory. Novel backgrounds exhibiting metal-insulator transitions (MIT) have been constructed in which both metallic phase and insulating phase have vanishing entropy density in zero temperature limit. We find that the first order derivative of HEE with respect to lattice parameters exhibits extremal behavior near QCPs. We propose that it would be a universal feature that HEE or its derivatives with respect to system parameters can characterize QPT in a generic holographic system. Our work opens a window for understanding the relation between entanglement and the QPT from a holographic perspective.
The interplay of the constituents of interacting many-body systems may reveal emergent properties on the macroscopic scale which are not inherent to the individual constituents. These properties are expressed in macroscopic observables \ndescribing the state — denoted as the phase of the system. Continuous phase transition between phases are generically manifested in critical behavior, for example, a divergence of a macroscopic observable. The identification of the present phase of a system and the classification of critical phenomena into universality classes are exciting challenges of condensed-matter physics. \nIn this thesis, we use entanglement entropies as macroscopic quantities for the characterization of phases of quantum matter and critical theories. For groundstates of quantum many-body systems the entanglement entropy is a measure of \nthe amount of entanglement between two subsystems. The generic dependence of the entanglement entropy on the size and shape of the subsystems is contained in the well-known boundary law — stating a scaling of the entanglement entropy with the boundary between the two subsystems. We numerically investigate how the coefficient of this dependence reflects quantum phase transitions in simple spin-half bilayer models. \nSubleading terms to the boundary law such as a logarithmic contribution provide universal numbers for the criticality of field theories. We examine free and interacting theories from an entanglement entropy perspective in order to assess the role of the coefficient of the logarithmic correction induced by corners in the subsystems. Beyond its universality, this coefficient also quantifies degrees of freedom of low-lying excitations in the conformal field theory describing a critical point. \nA constant contribution to the boundary law indicates the presence of so-called topological order in the ground state of a many-body system. This extremely useful property can also be identified in classical counterparts of entanglement entropy which we study at the example of various toric code models. To this endeavor, we have designed Monte Carlo techniques which allow for an efficient numerical computation of the constant contribution. In particular, we analyze via entanglement entropies under which conditions remnants of topological order are present in the quantum system at finite temperature and at perturbations from a magnetic field. The major motivation behind this effort is to use topological order for the robust storage of a quantum information — a basic need for the construction of quantum \ncomputers.
Critical phenomena, characterized by abrupt changes in the macroscopic properties of a system, exhibit a profound degree of universality, meaning that vastly different physical systems can display identical behavior near their critical points. This universality is typically understood through the lens of scaling laws and the Renormalization Group theory, which classify critical points into distinct universality classes. This paper proposes and explores the "Entropic Law of Critical Universality," an overarching principle positing that not only do thermodynamic quantities scale universally, but the fundamental information-theoretic measures of a system, particularly entropy in its various forms (thermodynamic entropy, entanglement entropy, Renyi entropy), also conform to universal scaling behaviors that uniquely characterize these universality classes. We review how entanglement entropy exhibits universal logarithmic corrections at quantum critical points, linked to the central charge of underlying conformal field theories. We also discuss how specific entropy behaves non-monotonically near quantum chromodynamics critical points and how entropic measures can identify phase transitions and their classes in various condensed matter systems, including graphene and spin models. The paper synthesizes theoretical frameworks and empirical evidence to demonstrate that entropy serves as a powerful and often more direct probe of the universal properties underlying critical phenomena, offering a comprehensive perspective on the shared information landscape of diverse critical systems.
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.