Bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect

Abstract

The Heisenberg model for spin-1 bosons in one dimension presents many different quantum phases including the famous topological Haldane phase. Here we study the robustness of such phases in front of a SU(2) symmetry breaking field as well as the emergence of novel phases. Previous studies have analyzed the effect of such uniaxial anysotropy in some restricted relevant points of the phase diagram. Here we extend those studies and present the complete phase diagram of the spin-1 chain with uniaxial anysotropy. To this aim, we employ the density matrix renormalization group (DMRG) together with analytical approaches. The complete phase diagram can be realized using ultracold spinor gases in the Mott insulator regime under a quadratic Zeeman effect.

Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy

“…Figure 5 presents how the individual components of the non-local correlations change over time for various values of the uniaxial anisotropy. order parameter are in agreement with earlier reported data [23].…”

Rhombi-chain Bose-Hubbard model: Geometric frustration and interactions

“…Before turning to the entanglement spectrum analysis, let us mention that the entropy scaling across the PLL-LL transition at finite deviations from φ = π is not displaying any clear signature of a c = 3/2 CFT line, as one would expect from its predicted Ising character 42,59 . The difficulties in analysing transitions between gapless phases has already been noticed in spin models 95 .…”

Symmetry restoring and ancilla-driven entanglement for ultra-cold spin-1 atoms in a three-site ring

“…(33) and (34) (see "Appendix 2"). However, for more general cases, the numerical calculations should be performed.…”

“…From the model point of view, the angle θ (ϕ) is confined within the interval (−π, π) and the experimental scheme where a whole range of θ (ϕ) can be obtained was also proposed. It can be done directly (for instance by using optical Feshbach resonances [39,40]) or by performing some kind of "quantum simulation" technique for which the system is initially prepared in its excited state (as it was proposed in [24,33]). Therefore, in contrast to the usual condensed matter systems, for ultra-cold atoms systems it becomes possible to engineer experimental setups for which biquadratic coupling is stronger than a quadratic one.…”

“…It is known that for the low energy limit, the interatomic interactions can be characterized by the s-wave scattering length which (in general) depends on the spin states in the incoming and outcoming scattering channels. Such spin-dependent interactions favor various relative orientation of the atomic spins, i.e., various spin configurations (for the spin-1 system, see for instance [33]). Therefore, gaining information concerning the values of coupling parameters allows to determine the nature of a ground state.…”