Partial-state fidelity and quantum phase transitions induced by continuous level crossing

Kwok, Ho-Man; Ho, Connie Suk‐Han; Gu, Shi-Jian

doi:10.1103/physreva.78.062302

Cited by 21 publications

(18 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was realized consequently that the leading term of the fidelity, called the FS [9] or the Riemannian metric tensor [10], should play a key role in such a new approach to QPTs. After that, various issues based on the fidelity or its leading term [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] , including scaling and universality class [13,14], and its role in topological QPTs [23][24][25][26] etc, were raised and addressed. However, it seems to us that all relevant studies took it for granted that the FS, in general quantum phases, has dimension d, i.e.,χ F ∝ L d where d(L) is the dimension (length) of the system.…”

mentioning

confidence: 99%

Scaling dimension of fidelity susceptibility in quantum phase transitions

Lin

2009

Europhys. Lett.

Self Cite

View full text Add to dashboard Cite

We analyze ground-state behaviors of fidelity susceptibility (FS) and show that the FS has its own distinct dimension instead of real system's dimension in general quantum phases. The scaling relation of the FS in quantum phase transitions (QPTs) is then established on more general grounds. Depending on whether the FS's dimensions of two neighboring quantum phases are the same or not, we are able to classify QPTs into two distinct types. For the latter type, the change in the FS's dimension is a characteristic that separates two phases. As a non-trivial application to the Kitaev honeycomb model, we find that the FS is proportional to L 2 ln L in the gapless phase, while L 2 in the gapped phase. Therefore, the extra dimension of ln L can be used as a characteristic of the gapless phase.

show abstract

mentioning

confidence: 99%

Scaling dimension of fidelity susceptibility in quantum phase transitions

Lin

2009

Europhys. Lett.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The advantage of utilizing a fidelity measure, originating from the quantum information concepts, to analyzing PTs is that it is state independent and no prior knowledge about order parameters is required. The fidelity susceptibility has been shown to contain sufficient information to reveal the universality class of the PTs [34], even for topological PTs [35], Kosterlitz-Thouless transitions [34], and PTs characterized by an underlying continuous level crossing [36]. The idea is simple, letting the ground state be parameterized by some quantity h (in our case h = ∆), ρ(h) = |Ψ(h) Ψ(h)| we introduce the reduced density operator for the internal states ρ A (h) = Tr B [ρ(h)], where the trace is over external degrees of freedom.…”

Section: A Sweep Through the Critical Pointmentioning

confidence: 99%

Dynamical quantum phase transition of a two-component Bose-Einstein condensate in an optical lattice

2010

View full text Add to dashboard Cite

We study the dynamics of a two-component Bose-Einstein condensate where the two components are coupled via an optical lattice. In particular, we focus on the dynamics as one drives the system through a critical point of a first-order phase transition characterized by a jump in the internal populations. Solving the time-dependent Gross-Pitaevskii equation, we analyze the breakdown of adiabaticity, impact of nonlinear atom-atom scattering, and role of a harmonic trapping potential. Our findings demonstrate that the phase transition is resilient to both contact interaction between atoms and external trapping confinement.

show abstract

“…In addition, the reduced fidelity and its susceptibility were also suggested in the studies of QPTs [27][28][29][30]. The reduced fidelity concerns the similarity of a local region of the system with respect to the driving parameter.…”

Section: Introductionmentioning

confidence: 99%

Fidelity susceptibility in two-dimensional spin-orbit models

You

Dong

2011

Phys. Rev. B

View full text Add to dashboard Cite

We study the quantum phase transitions in the two-dimensional spin-orbit models in terms of fidelity susceptibility and reduced fidelity susceptibility. An order-to-order phase transition is identified by fidelity susceptibility in the two-dimensional Heisenberg XXZ model with Dzyaloshinsky-Moriya interaction on a square lattice. The finite size scaling of fidelity susceptibility shows a power-law divergence at criticality, which indicates the quantum phase transition is of second order. Two distinct types of quantum phase transitions are witnessed by fidelity susceptibility in Kitaev-Heisenberg model on a hexagonal lattice. We exploit the symmetry of two-dimensional quantum compass model, and obtain a simple analytic expression of reduced fidelity susceptibility. Compared with the derivative of ground-state energy, the fidelity susceptibility is a bit more sensitive to phase transition. The violation of power-law behavior for the scaling of reduced fidelity susceptibility at criticality suggests that the quantum phase transition belongs to a first-order transition. We conclude that fidelity susceptibility and reduced fidelity susceptibility show great advantage to characterize diverse quantum phase transitions in spin-orbit models.

show abstract

Partial-state fidelity and quantum phase transitions induced by continuous level crossing

Cited by 21 publications

References 28 publications

Scaling dimension of fidelity susceptibility in quantum phase transitions

Scaling dimension of fidelity susceptibility in quantum phase transitions

Dynamical quantum phase transition of a two-component Bose-Einstein condensate in an optical lattice

Fidelity susceptibility in two-dimensional spin-orbit models

Contact Info

Product

Resources

About