String and conventional order parameters in the solvable modulated quantum chain

Chitov, Gennady Y.; Pandey, Toplal; Timonin, P. N.

doi:10.1103/physrevb.100.104428

Cited by 15 publications

(49 citation statements)

References 75 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The effective Hamiltonian of the columnar ladder is mapped onto two equivalent dimerized XY chains in a staggered transverse field (45,46). Contrary to the previous case, the columnar ladder has identical spectra in the even and odd sectors, resulting in the two-fold degeneracy of the eigenvalues of the Hamiltonisan (40). As a consequence, the phase diagram of this case is simpler, since there are no regions in the parametric space where different orders in the even and odd sectors overlap, resulting in larger variety of phases in Fig.…”

Section: Columnar Laddermentioning

confidence: 99%

“…The line pursued in the present study is that the extended Landau theory which incorporates the notions of nonlocal (string) order [37] and spontaneous breaking of hidden symmetry [38], remains instrumental even for nonconventional orders [14,[39][40][41]. The local and nonlocal string order parameters in the extended formalism are related by duality, and probing a phase transition and related emerging order is a problem of appropriate choice of variables [14,[39][40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Brane order and quantum magnetism in modulated anisotropic ladders

Pandey¹,

Chitov²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Two-leg spin-1 2 ladders with anisotropy and two different dimerization patterns are analyzed at zero temperature. This model is equivalent to a modulated interacting (Kitaev) ladder. The Hartree-Fock mean-field approximation reduces the model to a sum of two quadratic effective Majorana Hamiltonians, which are dual to a sum of two (even/odd) XY quantum chains in the alternating transverse fields. The mapping between the effective Hamiltonian of the ladder and the pair of the dual XY chains considerably simplifies calculations the order parameters and analysis of the hidden symmetry breaking. The ground-state phase diagram of the staggered ladder contains nine phases, four of them are conventional antiferromagnets, while the other five possess non-local brane orders. Using the dualities and the newly found exact results for the local and string order parameters of the transverse XY chains, we were able to find analytically all the magnetizations and the brane order parameters for the staggered case, as functions of the renormalized couplings of the effective Hamiltonian. The columnar ladder has three ground-state phases and does not possess magnetic long-ranged order. The brane order parameters for these three phases are calculated numerically from the Toeplitz determinants. We expect this study to motivate the search for the real spin-Peierls anisotropic ladder compounds which can undergo the predicted quantum phase transitions with gap closures and distinct brane orders.

show abstract

Section: Columnar Laddermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Brane order and quantum magnetism in modulated anisotropic ladders

Pandey¹,

Chitov²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…A characteristic feature of topological insulator is the edge or surface states occurring in the topologically nontrivial phase characterized by the nontrivially topological index, and the existence of the topological phase transition is generally accompanied by the changes of the topological numbers [5][6][7][8] or a nonlocal string order parameter. [9][10][11][12][13][14][15][16] The edge or surface states are protected by the energy gap of the topological system, leading that the edge states are robust against the local disorder and perturbation. [1,2,[17][18][19] These novel properties enable the topological insulator to have various potential applications in topological quantum simulation.…”

Section: Introductionmentioning

confidence: 99%

Topological Phase Transition and Topological Quantum State Transfer in Periodically Modulated Circuit‐QED Lattice

Cao

Cui

et al. 2021

Annalen der Physik

View full text Add to dashboard Cite

The topological properties of a circuit‐QED lattice are studied and it is found that the system undergoes a topological phase transition accompanied by the changes of Chern numbers from 2 to −1. For different lattice sizes, the energy eigenvalue spectra and the probability distributions of edge states are shown. Moreover, it is revealed that, depending on the strictly adiabatic evolution of the time‐dependent Hamiltonian, several different topological quantum state transfers between the first two sites and the last two sites can be achieved by employing the topologically protected edge states as the transfer channels. Further, it is demonstrated that, by using resonator‐based input–output process, the photonic topological edge state can be detected by measuring the average photon number in the steady state. The scheme opens up a new prospect for investigating the potential application of topological matter in quantum information processing.

show abstract

“…The simplest model for quasi-periodicity is the Harper model [56] with a cosine-like shaped potential, which has been considered in Kitaev chains [35,38,51,53]. It can also be demonstrated that this model is closely related to the anisotropic XY spin chain (AXYSC) through the Jordan-Wigner (J-W) transformation [57][58][59][60][61][62][63][64]. One is then interesting in more nontrivial case.…”

Section: Introductionmentioning

confidence: 99%

Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials

Huang,

Yao

2021

Preprint

View full text Add to dashboard Cite

By using the variational matrix product state method, we numerically study the interacting Kitaev chain with spatially varying periodic and quasi-periodic potentials and the latter follows the Fibonacci sequence. The edge correlation functions of Majorana fermions and low-lying ground states are computed to explore the robustness of topological superconducting phase. It is found that the original topological nontrivial phase is separated into to two branches by an emergent topological trivial phase, as a result of the competition among spatially varying potential, electronic Coulomb interaction and chemical potential. The analysis of energy gap and occupation number together suggests that the spontaneous symmetry breaking and the lift of degeneracy in the topological trivial phase are enabled by a potential-induced Fracton mechanism, namely the pairing of four Majorana fermions. It can be broken by further enhancing the interaction, and then the nontrivial phase reemerges. The evolution from the emergent fractal structure of population outside the critical region to the original structure of charge density wave is investigated as well.

show abstract

String and conventional order parameters in the solvable modulated quantum chain

Cited by 15 publications

References 75 publications

Brane order and quantum magnetism in modulated anisotropic ladders

Brane order and quantum magnetism in modulated anisotropic ladders

Topological Phase Transition and Topological Quantum State Transfer in Periodically Modulated Circuit‐QED Lattice

Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials

Contact Info

Product

Resources

About