QUANTUM PHASE TRANSITIONS AND EVENT HORIZONS: CONDENSED MATTER ANALOGIES

2006 ◽  
Author(s):  
GEORGE CHAPLINE
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Condensed Matter ◽  
Quantum Phase ◽  
Event Horizons

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.

QUANTUM PHASE TRANSITIONS AND EVENT HORIZONS: CONDENSED MATTER ANALOGIES

2006 ◽  
Vol 20 (19) ◽  
pp. 2647-2650
Author(s):  
GEORGE CHAPLINE
Keyword(s):  
General Relativity ◽  
Phase Transitions ◽  
Event Horizon ◽  
Thought Experiment ◽  
Quantum Phase Transitions ◽  
Martensitic Transformations ◽  
Space Time ◽  
Quantum Phase ◽  
Event Horizons ◽  
Heavy Fermion Materials

Although it has been generally believed that classical general relativity is always correct for macroscopic length scales, certain predictions such as event horizons and closed time-like curves are inconsistent with ordinary quantum mechanics. It has recently been pointed out that the event horizon problem can be resolved if space-time undergoes a quantum phase transition as one approaches the surface where general relativity predicts that the redshift becomes infinite. Indeed a thought experiment involving a superfluid with a critical point makes such a suggestion appear plausible. Furthermore the behavior of space-time near an event horizon may resemble quantum phase transitions that have been observed in the laboratory. For example, the phenomenology of metamagnetic quantum critical points in heavy fermion materials resembles the behavior expected, both in terms of time standing still and the behavior of quantum correlation functions. Martensitic transformations accompanied by non-adiabatic changes in the electronic wave function are also interesting in this connection.

Quantum phase transitions

2004 ◽  
Vol 174 (8) ◽  
pp. 853 ◽  
Author(s):  
Sergei M. Stishov
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Phase

scholarly journals Magnetic Field- and Pressure-Induced Quantum Phase Transitions in NH4CuCl3

2005 ◽  
Vol 159 ◽  
pp. 241-245 ◽  
Author(s):  
Masashi Fujisawa ◽  
Budhy Kurniawan ◽  
Toshio Ono ◽  
Hidekazu Tanaka
Keyword(s):  
Magnetic Field ◽  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Phase

scholarly journals Interaction between Different Kinds of Quantum Phase Transitions

2021 ◽  
Vol 3 (2) ◽  
pp. 253-261
Author(s):  
Angel Ricardo Plastino ◽  
Gustavo Luis Ferri ◽  
Angelo Plastino
Keyword(s):  
Phase Transitions ◽  
Nuclear Physics ◽  
Body Problem ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Many Body ◽  
Pairing Interaction ◽  
Exactly Solvable

We employ two different Lipkin-like, exactly solvable models so as to display features of the competition between different fermion–fermion quantum interactions (at finite temperatures). One of our two interactions mimics the pairing interaction responsible for superconductivity. The other interaction is a monopole one that resembles the so-called quadrupole one, much used in nuclear physics as a residual interaction. The pairing versus monopole effects here observed afford for some interesting insights into the intricacies of the quantum many body problem, in particular with regards to so-called quantum phase transitions (strictly, level crossings).

Sign in / Sign up

Export Citation Format

Share Document