scholarly journals The Loschmidt Index

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Diego Liska ◽  
Vladimir Gritsev
Keyword(s):  
Phase Transitions ◽  
Integral Representation ◽  
Quantum Phase Transitions ◽  
Ground States ◽  
Quantum Phase ◽  
Xy Model ◽  
Parameter Dependent ◽  
The Relationship ◽  
Multi Band

We study the nodes of the wavefunction overlap between ground states of a parameter-dependent Hamiltonian. These nodes are topological, and we can use them to analyze in a unifying way both equilibrium and dynamical quantum phase transitions in multi-band systems. We define the Loschmidt index as the number of nodes in this overlap and discuss the relationship between this index and the wrapping number of a closed auxiliary hypersurface. This relationship allows us to compute this index systematically, using an integral representation of the wrapping number. We comment on the relationship between the Loschmidt index and other well-established topological numbers. As an example, we classify the equilibrium and dynamical quantum phase transitions of the XY model by counting the nodes in the wavefunction overlaps.

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 fidelity for degenerate ground states in quantum phase transitions

2013 ◽  
Vol 88 (3) ◽  
Author(s):  
Yao Heng Su ◽  
Bing-Quan Hu ◽  
Sheng-Hao Li ◽  
Sam Young Cho
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Ground States ◽  
Quantum Phase ◽  
Quantum Fidelity

scholarly journals GROUND STATES OF A MIXTURE OF TWO SPECIES OF SPIN-1 BOSE GASES WITH INTERSPECIES SPIN EXCHANGE IN A MAGNETIC FIELD

2012 ◽  
Vol 26 (01) ◽  
pp. 1250002 ◽  
Author(s):  
YU SHI ◽  
LI GE
Keyword(s):  
Magnetic Field ◽  
Phase Diagram ◽  
Phase Transitions ◽  
Spin Exchange ◽  
Quantum Phase Transitions ◽  
Ground States ◽  
Total Spin ◽  
Quantum Phase ◽  
Spin Coupling ◽  
The Magnetic Field

We consider a mixture of two species of spin-1 atoms with both interspecies and intraspecies spin exchanges in a weak magnetic field. Under the usual single mode approximation, it can be reduced to a model of coupled giant spins. We find most of its ground states. This is a complicated problem of energy minimization, with three quantum variables under constraints, i.e., the total spin of each species and the total spin of the whole mixture, as well as four parameters, including intraspecies and interspecies spin coupling strengths and the magnetic field. The quantum phase diagram is very rich. Compared with the case without a magnetic field, the ground states are modified by a magnetic field, which also modifies the ground state boundaries or introduces new crossover regimes on the phase diagram. Without interspecies spin coupling, the quantum phase transitions existing in absence of a magnetic field disappear when a magnetic field is applied, which leads to crossover regimes in the phase diagram. Under ferromagnetic interspecies spin coupling, the ground states remain disentangled no matter whether there is a magnetic field. For antiferromagnetic interspecies spin coupling, a magnetic field entangles the ground states in some parameter regimes. When the intraspecies spin couplings are both ferromagnetic, the quantum phase transition between antiferromagnetic and zero interspecies spin couplings survives the magnetic field. When the intraspecies spin couplings are both antiferromagnetic, a magnetic field induces new quantum phase transitions between antiferromagnetic and zero interspecies spin couplings.

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