Replacing energy by von Neumann entropy in quantum phase transitions

Abstract

In the thermodynamic limit two distinct states of matter cannot be analytic continuations of each other. Classical phase transitions are characterized by non-analyticities of the free energy. For quantum phase transitions (QPTs) the ground state energy often assumes the role of the free energy. But in a number of important cases this criterion fails to predict a QPT, such as the three-dimensional metal-insulator transition of non-interacting electrons in a random potential (Anderson localization). It is therefore essential that we find alternative criteria that can track fundamental changes in the internal correlations of the ground state wavefunction. Here we propose that QPTs are generally accompanied by non-analyticities of the von Neumann (entanglement) entropy. In particular, the entropy is non-analytic at the Anderson transition, where it exhibits unusual fractal scaling. We also examine two dissipative quantum systems of considerable interest to the study of decoherence and find that non-analyticities occur if and only if the system undergoes a QPT.

8 pages, 6 figures; Annals of Physics, in press (2006)

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• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Entanglement and Criticality in Quantum Impurity Systems
• Criticality and entanglement in random quantum systems
• Quantum Impurity Entanglement
• Entanglement entropy and multifractality at localization transitions
• Characterizing disordered fermion systems using the momentum-space entanglement spectrum
• Scaling of Entanglement Entropy at 2D quantum Lifshitz fixed points and topological fluids
• Separation-dependent localization in a two-impurity spin-boson model
• Maximally Entangled Mode, Metal-Insulator Transition and Violation of Entanglement Area Law in Non-interacting Fermion Ground States
• Quantum-entanglement aspects of polaron systems
• Scaling of von Neumann entropy at the Anderson transition
• Quantum phase transitions in a charge-coupled Bose-Fermi Anderson model
• Entanglement entropy and particle number cumulants of disordered fermions
• Non-Markovian dynamical effects and time evolution of entanglement entropy of a dissipative two-state system
• Quantum tricritical point emerging in the spin-boson model with two dissipative spins in staggered biases
• Entanglement in Disordered Systems at Criticality
• Entanglement entropy of a quantum unbinding transition and entropy of DNA
• A new signature of quantum phase transitions from the numerical range
• Entanglement of spin chains with general boundaries and of dissipative systems
• von Neumann entropy and on-site localization for perpetually coupled qubits
• Quantum steering ellipsoids and quantum obesity in critical systems