Entropic signature of quantum phase transitions in low-dimensional models

Örs Legeza, Jenő Sólyom, L. Tincani +1 more

We propose a new approach to study quantum phase transitions in low-dimensional fermionic or spin models that go from uniform to spatially inhomogeneous phases such as dimerized, trimerized, or incommensurate phases. It is based on studying the length dependence of the von Neumann entropy and its corresponding Fourier spectrum for finite segments in the ground state of finite chains. Peaks at a nonzero wave vector are indicators of oscillatory behavior in decaying correlation functions and also provide significant information about certain relevant features of the excitation spectrum; in particular, they can identify the wave vector of soft modes in critical models.

Kazuo Ueda, 上田 和夫

Laurent Sanchez-Palencia

Cheng‐Cheng Liu, Ze-Wei Sun, Xiao‐Gang Fan +4 more

Uncertainty principle establishes a remarkable lower bound to predict the measured outcome of two non-commuting observables. In this paper, based on the quantum renormalization-group method, we study the relation between quantum-memory-assisted entropic uncertainty relation (QMA-EUR) and quantum phase transition (QPT) in the spin XXZ model. The results shows that the entropic uncertainty and the lower bound have similar traits. In addition, we propose two schemes, one is based on quantum discord and classical correlation, the other Holevo quantity and mutual information, both can tighten the bound of EUR in the presence of quantum memory. The tighter the entropy uncertainty relationship is, the higher the accuracy of the predicted results will be. Moreover, we can obtain the optimal lower bound with the help of Holevo quantity and mutual information, which have the best optimization effect in this model. Additionally, we study QPT by virtue of EUR and after a certain number of iterations, finding that the value of QMA-EUR of the whole block-block state can form two saturated values, which are related to two different phases: spin-fluid phase and Néel phase. Afterwards, we discover that the QMA-EUR of the block-block state obeys the nonanalytic and scaling properties with entropic uncertainty relation exponent associated with correlation length. Our findings show that QMA-EUR deserves to be used as an effective tool in reflecting quantum criticality for more quantum many-body systems and may also shed light on many applications in quantum physics including the quantum key distribution, the detection of QPT and the evaluation of the capacity of quantum computation in critical systems.

А. А. МЛ. ЖАРОВ

Asmi Haldar, Krishnanand Mallayya, Markus Heyl +3 more

Quantum phase transitions are central to our understanding of why matter at very low temperatures can exhibit starkly different properties upon small changes of microscopic parameters.Accurately locating those transitions is challenging experimentally and theoretically.Here, we show that the antithetic strategy of forcing systems out of equilibrium via sudden quenches provides a route to locate quantum phase transitions.Specifically, we show that such transitions imprint distinctive features in the intermediate-time dynamics, and results after equilibration, of local observables in quantum chaotic spin chains.Furthermore, we show that the effective temperature in the expected thermal-like states after equilibration can exhibit minima in the vicinity of the quantum critical points.We discuss how to test our results in experiments with Rydberg atoms and explore nonequilibrium signatures of quantum critical points in models with topological transitions.