Sign structure, electron fractionalization, and emergent gauge description of the Hubbard model

Zhang, Long; Weng, Zheng-Yu

doi:10.1103/physrevb.90.165120

Cited by 19 publications

(20 citation statements)

References 33 publications

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“…This σ -Hubbard model has been previously studied in ref. 34 , which differs from the Hubbard model by a Berry-like phase 33 (phase string) as to be discussed in Sec. II E below.…”

Section: Many-body Localization In the Hubbard Modelmentioning

confidence: 99%

“…Specifically, the phase string effect in the bipartite Hubbard model is manifested in the partition function as follows: 33 At any temperature and doping,…”

Section: Many-body Localization In the Hubbard Modelmentioning

confidence: 99%

“…where the weight ( c ) ≥ 0 for any closed path c of displacements of holons (empty sites), doublons (doubly occupied sites) and spins (singly occupied sites). Here the phase string sign structure is Berry-phase-like as given by 33 …”

Section: Many-body Localization In the Hubbard Modelmentioning

confidence: 99%

“…As such, the charge sector of lightly doped Hubbard model with sufficiently large but finite U has an emergent MBL violating ETH and with spontaneous translational symmetry breaking in finite energy-density states. Further, an eigenstate phase transition to a conventional delocalized phase has been found by increasing the anisotropy of the hopping integrals of the ladder or by turning off the so-called phase strings 33 34 as the intrinsic Berry phase of the Hubbard model.…”

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confidence: 99%

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On the possibility of many-body localization in a doped Mott insulator

Weng

2016

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Many-body localization (MBL) is currently a hot issue of interacting systems, in which quantum mechanics overcomes thermalization of statistical mechanics. Like Anderson localization of non-interacting electrons, disorders are usually crucial in engineering the quantum interference in MBL. For translation invariant systems, however, the breakdown of eigenstate thermalization hypothesis due to a pure many-body quantum effect is still unclear. Here we demonstrate a possible MBL phenomenon without disorder, which emerges in a lightly doped Hubbard model with very strong interaction. By means of density matrix renormalization group numerical calculation on a two-leg ladder, we show that whereas a single hole can induce a very heavy Nagaoka polaron, two or more holes will form bound pair/droplets which are all localized excitations with flat bands at low energy densities. Consequently, MBL eigenstates of finite energy density can be constructed as composed of these localized droplets spatially separated. We further identify the underlying mechanism for this MBL as due to a novel ‘Berry phase’ of the doped Mott insulator, and show that by turning off this Berry phase either by increasing the anisotropy of the model or by hand, an eigenstate transition from the MBL to a conventional quasiparticle phase can be realized.

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“…This σ -Hubbard model has been previously studied in ref. 34 , which differs from the Hubbard model by a Berry-like phase 33 (phase string) as to be discussed in Sec. II E below.…”

Section: Many-body Localization In the Hubbard Modelmentioning

confidence: 99%

“…Specifically, the phase string effect in the bipartite Hubbard model is manifested in the partition function as follows: 33 At any temperature and doping,…”

Section: Many-body Localization In the Hubbard Modelmentioning

confidence: 99%

Section: Many-body Localization In the Hubbard Modelmentioning

confidence: 99%

mentioning

confidence: 99%

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On the possibility of many-body localization in a doped Mott insulator

Weng

2016

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“…The precise sign structure for the Hubbard model has recently been rigorously worked out [15]. Specifically, the partition function of the Hubbard model can be expressed as [15] …”

Section: Origin Of Spin and Charge Modulations: Phase-string Effmentioning

confidence: 99%

Spin and charge modulations in a single-hole-doped Hubbard ladder: Verification with optical lattice experiments

Zhu

Weng

2016

Phys. Rev. A

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We show that pronounced modulations in spin and charge densities can be induced by the insertion of a single hole in an otherwise half-filled two-leg Hubbard ladder. Accompanied with these modulations is a loosely bound structure of the doped charge with a spin-1/2, in contrast to the tightly bound case where such modulations are absent. These behaviors are caused by the interference of the Berry phases associated with a string of flipped spins (or "phase strings") left behind as a hole travels through a spin bath with a short-range antiferromagnetic order. The key role of the phase strings is also reflected in how the system responds to increasing spin polarization and the on-site repulsion, addition of a second hole, and increasing asymmetry between intra-and interchain hopping. Remarkably, all these properties persist down to ladders as short as ∼10 sites, as the smoking gun of the phase-string effect. They can therefore be studied in cold-atom experiments using the recently developed fermion microscope.

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Charge-spin mutual entanglement: A case study by exact diagonalization of the one hole doped t-J loop

Zheng¹,

Weng²

2018

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We investigate the ground state and excitations of finite-size Heisenberg loops doped with one hole as the simplest example to illustrate the nature of strong correlations in a doped Mott insulator. We show that the doped hole form a peculiar long-range entanglement with the surrounding spins as revealed by inspecting the mutual correlations between the charge and spin using exact diagonalization (ED). In particular, the one-hole ground state acquires a series of non-trivial total momenta depending on the ratio J/t (J and t denote the superexchange coupling and hopping integral, respectively), which gives rise to distinct quantum phases separated by critical points (CPs). Interestingly the novel total momentum and correlations completely disappear once a singular sign structure is turned off in the t-J model, indicating the latter is the true original source for strong correlation via many-body quantum interference. We emphasize that the novelties discovered here are not restricted to the one-dimensional loop. We introduce a new charge-spin mutual entanglement that can well characterize these exotic properties, which can be then easily generalized to more realistic situations like two dimensions.

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Sign structure, electron fractionalization, and emergent gauge description of the Hubbard model

Cited by 19 publications

References 33 publications

On the possibility of many-body localization in a doped Mott insulator

On the possibility of many-body localization in a doped Mott insulator

Spin and charge modulations in a single-hole-doped Hubbard ladder: Verification with optical lattice experiments

Charge-spin mutual entanglement: A case study by exact diagonalization of the one hole doped t-J loop

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