Many quantum condensed-matter systems, and probably the quantum vacuum of our Universe, are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the low-energy does not depend on the complicated details of the system and is relatively simple. It is determined by the nodes in the fermionic spectrum, which are protected by topology in momentum space (in some cases, in combination with the vacuum symmetry). Here we illustrate this universality on some examples of quantum phase transitions, which can occur between the vacua with the same symmetry but with diferent topology in momentum space. The quantum phase transitions between the fully gapped states with different momentum-space topology are also discussed.Many quantum condensed-matter systems, and probably the quantum vacuum of our Universe, are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the low-energy does not depend on the complicated details of the system and is relatively simple. It is determined by the nodes in the fermionic spectrum, which are protected by topology in momentum space (in some cases, in combination with the vacuum symmetry). Here we illustrate this universality on some examples of quantum phase transitions, which can occur between the vacua with the same symmetry but with diferent topology in momentum space. The quantum phase transitions between the fully gapped states with different momentum-space topology are also discussed.

arXiv:cond-mat/0505089May 4, 20050 citations

Topological phases and phase transitions in a two-dimensional fermionic lattice

C. Morais Smith, Wouter Beugeling, Nathan Goldman

Bulletin of the American Physical SocietyFeb 27, 20120 citations

Topological quantum phase transition in the BEC-BCS crossover

Mitsuhiro Arikawa, Isao Maruyama, Yasuhiro Hatsugai

A crossover between the Bose-Einstein condensation (BEC) and BCS superconducting state is described topologically in the chiral symmetric fermion system with attractive interaction. Using a local ${Z}_{2}$ Berry phase, we found a quantum phase transition between the BEC and BCS phases without accompanying the bulk gap closing.A crossover between the Bose-Einstein condensation (BEC) and BCS superconducting state is described topologically in the chiral symmetric fermion system with attractive interaction. Using a local ${Z}_{2}$ Berry phase, we found a quantum phase transition between the BEC and BCS phases without accompanying the bulk gap closing.

arXiv:1003.4735Physical Review BAug 30, 201010 citations

Topological Quantum Phase Transitions and Quench Dynamics

Shiuan-Fan Liou

Jan 1, 20190 citations

Quasiparticles in condensed matter systems

P. Wölfle

Quasiparticles are a powerful concept of condensed matter quantum theory. In this review, the appearence and the properties of quasiparticles are presented in a unifying perspective. The principles behind the existence of quasiparticle excitations in both quantum disordered and ordered phases of fermionic and bosonic systems are discussed. The lifetime of quasiparticles is considered in particular near a continuous classical or quantum phase transition, when the nature of quasiparticles on both sides of a transition into an ordered state changes. A new concept of critical quasiparticles near a quantum critical point is introduced, and applied to quantum phase transitions in heavy fermion metals. Fractional quasiparticles in systems of restricted dimensionality are reviewed. Dirac quasiparticles emerging in so-called Dirac materials are discussed. The more recent discoveries of topologically protected chiral quasiparticles in topological matter and Majorana quasiparticles in topological superconductors are briefly reviewed.Quasiparticles are a powerful concept of condensed matter quantum theory. In this review, the appearence and the properties of quasiparticles are presented in a unifying perspective. The principles behind the existence of quasiparticle excitations in both quantum disordered and ordered phases of fermionic and bosonic systems are discussed. The lifetime of quasiparticles is considered in particular near a continuous classical or quantum phase transition, when the nature of quasiparticles on both sides of a transition into an ordered state changes. A new concept of critical quasiparticles near a quantum critical point is introduced, and applied to quantum phase transitions in heavy fermion metals. Fractional quasiparticles in systems of restricted dimensionality are reviewed. Dirac quasiparticles emerging in so-called Dirac materials are discussed. The more recent discoveries of topologically protected chiral quasiparticles in topological matter and Majorana quasiparticles in topological superconductors are briefly reviewed.

Reports on Progress in PhysicsNov 20, 201739 citations

A crossover between the Bose-Einstein condensation (BEC) and BCS superconducting state is described topologically in the chiral symmetric fermion system with attractive interaction. Using a local

{Z}_{2}

Berry phase, we found a quantum phase transition between the BEC and BCS phases without accompanying the bulk gap closing.