scholarly journals The Use of Entanglement Entropy to Classify Quantum Phase Transitions in 1D Ultracold Spinor Bosons

2018 ◽  
Vol 21 (1) ◽  
pp. 23 ◽  
Author(s):  
Karen Rodríguez Ramírez
Keyword(s):  
Phase Transitions ◽  
Central Charge ◽  
Quantum Phase Transitions ◽  
Condensed Matter ◽  
Entanglement Entropy ◽  
Lattice Models ◽  
Universality Class ◽  
Quantum Phases ◽  
The Matrix ◽  
Novel Method

In this paper, we discuss a novel method based on a quantum-information-toolsuitable to identify and characterize quantum-phases and phase transitions in a broad set of lattice models relevant in condensed-matter systems. The method relies on theentanglement entropy which, for instance, can be calculated using the Matrix ProductState (MPS) algorithm, or any other method, for several system sizes to perform an appropriate scaling. Particularly, this advanced method has been applied for a finite 1D system of repulsively interacting spin-1 bosons and obtaining the universality class via the calculation of the central charge for the extemal field-induced phase transitionbetween the dimerized phase and the XY-nematic phase in the antiferromagnetic regime.Finally, we briefly discuss how this method has been recently used to identify topologicalphases.

scholarly journals GEOMETRIC PHASES AND QUANTUM PHASE TRANSITIONS

2008 ◽  
Vol 22 (06) ◽  
pp. 561-581 ◽  
Author(s):  
SHI-LIANG ZHU
Keyword(s):  
Phase Transitions ◽  
Geometric Phase ◽  
Quantum Phase Transitions ◽  
Condensed Matter ◽  
Quantum Phase ◽  
Many Body ◽  
Scientific Communities ◽  
Geometric Phases ◽  
Many Body Systems ◽  
The Many

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed the so-called "criticality of geometric phase", in which the geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of the geometric quantities may open attractive avenues and fruitful dialogue between different scientific communities.

GENERALIZED ENTANGLEMENT AND QUANTUM PHASE TRANSITIONS

2006 ◽  
Vol 20 (19) ◽  
pp. 2760-2769 ◽  
Author(s):  
ROLANDO SOMMA ◽  
HOWARD BARNUM ◽  
EMANUEL KNILL ◽  
GERARDO ORTIZ ◽  
LORENZO VIOLA
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Condensed Matter ◽  
Transverse Magnetic ◽  
Quantum Phase ◽  
Broken Symmetry ◽  
Illustrative Case ◽  
One Dimensional ◽  
The Relationship ◽  
Qualitative Changes

Quantum phase transitions in matter are characterized by qualitative changes in some correlation functions of the system, which are ultimately related to entanglement. In this work, we study the second-order quantum phase transitions present in models of relevance to condensed-matter physics by exploiting the notion of generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)]. In particular, we focus on the illustrative case of a one-dimensional spin-1/2 Ising model in the presence of a transverse magnetic field. Our approach leads to tools useful for distinguishing between the ordered and disordered phases in the case of broken-symmetry quantum phase transitions. Possible extensions to the study of other kinds of phase transitions as well as of the relationship between generalized entanglement and computational efficiency are also discussed.

scholarly journals Quantum phases and quantum excitations in spin systems

Impact ◽  
2020 ◽  
Vol 2020 (5) ◽  
pp. 22-24
Author(s):  
Hidekazu Tanaka
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Effect ◽  
Elementary Excitation ◽  
Spin Systems ◽  
Magnetic Excitation ◽  
Quantum Phases ◽  
Tokyo Institute ◽  
Institute Of Technology ◽  
Quantum Phenomena

Professor Hidekazu Tanaka is based at the Department of Physics at the Tokyo Institute of Technology, Japan, where he is collaborating with a team of researchers to investigate magnetic quantum phenomena focusing on quantum phase transitions. Tanaka and his team have set about creating something they call a 'quantum magnetic excitation', which is essentially an elementary excitation that can be used on a quantum scale to explain how the quantum effect and multiple spins interact with one another. Their ultimate aim is to discover novel magnetic phenomena that occur at these scales and elucidate the mechanisms involved.

scholarly journals BCFT entanglement entropy at large central charge and the black hole interior

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
James Sully ◽  
Mark Van Raamsdonk ◽  
David Wakeham
Keyword(s):  
Black Hole ◽  
Phase Transitions ◽  
Single Channel ◽  
Central Charge ◽  
Black Hole Physics ◽  
Entanglement Entropy ◽  
Conformal Field ◽  
Boundary Operators ◽  
Black Hole Interior ◽  
Twist Operators

Abstract In this note, we consider entanglement and Renyi entropies for spatial subsystems of a boundary conformal field theory (BCFT) or of a CFT in a state constructed using a Euclidean BCFT path integral. Holographic calculations suggest that these entropies undergo phase transitions as a function of time or parameters describing the subsystem; these arise from a change in topology of the RT surface. In recent applications to black hole physics, such transitions have been seen to govern whether or not the bulk entanglement wedge of a (B)CFT region includes a portion of the black hole interior and have played a crucial role in understanding the semiclassical origin of the Page curve for evaporating black holes.In this paper, we reproduce these holographic results via direct (B)CFT calculations. Using the replica method, the entropies are related to correlation functions of twist operators in a Euclidean BCFT. These correlations functions can be expanded in various channels involving intermediate bulk or boundary operators. Under certain sparseness conditions on the spectrum and OPE coefficients of bulk and boundary operators, we show that the twist correlators are dominated by the vacuum block in a single channel, with the relevant channel depending on the position of the twists. These transitions between channels lead to the holographically observed phase transitions in entropies.

scholarly journals Exotic criticality in the dimerized spin-1 $XXZ$ chain with single-ion anisotropy

2018 ◽  
Vol 5 (6) ◽  
Author(s):  
Satoshi Ejima ◽  
Tomoki Yamaguchi ◽  
Fabian Essler ◽  
Florian Lange ◽  
Yukinori Ohta ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Critical Point ◽  
Phase Structure ◽  
Quantum Phase Transitions ◽  
Universality Class ◽  
Quantum Magnets ◽  
One Dimensional ◽  
Xxz Chain ◽  
Dilute Ising Model

We consider the dimerized spin-1 XXZ chain with single-ion anisotropy D. In absence of an explicit dimerization there are three phases: a large-$D$, an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.

Sign in / Sign up

Export Citation Format

Share Document