The bilinear–biquadratic model on the complete graph

Jakab, Dávid; Szirmai, G.; Zimborás, Zoltán

doi:10.1088/1751-8121/aaa92b

Cited by 5 publications

(4 citation statements)

References 62 publications

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“…Surprisingly, the precision bound is the same for any such state. PI singlet states are very relevant for experiments, since they have been experimentally created in cold gases [79,80] while they also appear in condensed matter physics [81].…”

Section: Singlet Statesmentioning

confidence: 99%

Precision bounds for gradient magnetometry with atomic ensembles

et al. 2018

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We study gradient magnetometry with an ensemble of atoms with arbitrary spin. We calculate precision bounds for estimating the gradient of the magnetic field based on the quantum Fisher information. For quantum states that are invariant under homogeneous magnetic fields, we need to measure a single observable to estimate the gradient. On the other hand, for states that are sensitive to homogeneous fields, a simultaneous measurement is needed, as the homogeneous field must also be estimated. We prove that for the cases studied in this paper, such a measurement is feasible. We present a method to calculate precision bounds for gradient estimation with a chain of atoms or with two spatially separated atomic ensembles. We also consider a single atomic ensemble with an arbitrary density profile, where the atoms cannot be addressed individually, and which is a very relevant case for experiments. Our model can take into account even correlations between particle positions. While in most of the discussion we consider an ensemble of localized particles that are classical with respect to their spatial degree of freedom, we also discuss the case of gradient metrology with a single Bose-Einstein condensate.

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Section: Singlet Statesmentioning

confidence: 99%

Precision bounds for gradient magnetometry with atomic ensembles

et al. 2018

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“…Another interesting generalization that does not involve the spatial redistribution of the couplings would be to study less symmetric interactions; a natural candidate would be reducing the SU(3) symmetry to SU(2). In the case of spin-1 this is described by the bilinear-biquadratic interaction, which has already been studied on complete graphs [33]. Symmetric collective spin states have been studied, due to their experimental feasibility, also from a quantum metrology point of view [43,44], it would be interesting to study also bipartite models especially in the light of the experiment reported in [45].…”

Section: Discussionmentioning

confidence: 99%

“…( 6) will be proportional to the quadratic Casimir operator of the global SU (3) spin operators, and hence its eigenproblem simplifies to determining how the entire Hilbert space decomposes into SU(3) irreducible representations (irreps). This was discussed in [32] and also in [33] as a special case of the bilinearbiquadratic model on the complete graph.…”

Section: The Model Hamiltonianmentioning

confidence: 99%

Quantum phases of collective SU(3) spin systems with bipartite symmetry

Jakab,

Zimborás

2020

Preprint

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We study a bipartite collective spin-1 model with exchange interaction between the spins. The bipartite nature of the model manifests itself by the spins being divided into two equal-sized subsystems; within each subsystem the spin-spin interactions are of the same strength, across the subsystems they are also equal, but the two coupling values within and across the subsystem are different. Such a set-up is inspired by recent experiments with ultracold atoms. Using the SU(3)symmetry of the exchange interaction and the permutation symmetry within the subsystems, we can employ representation theoretic methods to diagonalize the Hamiltonian of the system in the entire parameter space of the two coupling-strengths. These techniques then allow us to explicitly construct and explore the ground-state phase diagram. The phase diagram turns out to be rich containing both gapped and gapless phases. An interesting observation is that one of the five phases features a strong bipartite symmetry breaking, meaning that the two subsystems in the ground states are in different SU(3) representations.

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“…where 𝑆 i denotes the spin-1 operator at lattice site i, and α = tan φ is the control parameter. The model has been investigated extensively using analytical and numerical methods, [8][9][10][11][12][13][14][15][16][17][18][19][20] exhibiting rich physics. Its ground state phase diagram has been mostly understood.…”

Section: Introductionmentioning

confidence: 99%

Commensurate and incommensurate Haldane phases for a spin-1 bilinear–biquadratic model

et al. 2023

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The commensurate and incommensurate Haldane phases for the spin-1 bilinear-biquadratic model are investigated using the infinite matrix product state algorithm. The bipartite entanglement entropy can detect a transition point between the two phases. In both phases, the entanglement spectrum shows the double degeneracy. We calculate the nonlocal order parameter of the bond-centered inversion in both phases, which rapidly approaches a saturation value -1 as the segment length increases. The nonlocal order parameter of the bond-centered inversion with a saturation value -1 and the nonzero value string order indicate that the Haldane phase is a symmetry-protected topological phase. To distinguish the commensurate and incommensurate Haldane phases, the transversal spin correlation and corresponding momentum distribution of the structure factor are analyzed. As a result, the transversal spin correlations exhibit different decay forms in both phases.

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The bilinear–biquadratic model on the complete graph

Cited by 5 publications

References 62 publications

Precision bounds for gradient magnetometry with atomic ensembles

Precision bounds for gradient magnetometry with atomic ensembles

Quantum phases of collective SU(3) spin systems with bipartite symmetry

Commensurate and incommensurate Haldane phases for a spin-1 bilinear–biquadratic model

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