Topological phases arising from attractive interaction and pair hopping in the extended Hubbard model

Rausch, Roman; Peschke, Matthias

doi:10.1088/1367-2630/ab9c65

Cited by 7 publications

(5 citation statements)

References 46 publications

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“…If U(1) symmetries are exploited in the infinite system, there is to the best of our knowledge no practical way to compute the value of S tot /L in the M tot = 0 sector. In order to access S tot /L, we switch off the symmetry altogether [47]. Within the degenerate set of 2S tot + 1 states, the DMRG tends to converge to the M tot = S tot sector, whose entanglement is minimal.…”

Section: Infinite Systemsmentioning

confidence: 99%

Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

et al. 2023

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The ferrimagnetic phase of the sawtooth chain with mixed ferromagnetic nearest-neighbour interactions JJ and antiferromagnetic next-nearest-neighbour interactions J'J′ (within the isotropic Heisenberg model) was previously characterized as a phase with commensurate order. In this paper, we demonstrate that the system in fact exhibits an incommensurate quantum spin spiral. Even though the ground state is translationally invariant in terms of the local spin expectations ‹S_i›‹Si#8250;, the spiral can be detected via the connected spin-spin correlations ‹{S_i\cdot S_j}#8250;‹Si⋅Sj#8250;-‹{S_i}#8250;\cdot‹{S_j}#8250;‹Si#8250;⋅‹Sj#8250; between the apical spins. It has a long wavelength that grows with J'J′ and that soon exceeds finite-system sizes typically employed in numerical simulations. A faithful treatment thus requires the use of state-of-the-art simulations for large, periodic systems. In this work, we are able to accurately treat up to L=400L=400 sites (200 unit cells) with periodic boundary conditions using the density-matrix renormaliztion group (DMRG). Exploiting the SU(2) symmetry allows us to directly compute the lowest-energy state for a given total spin. Our results are corroborated by variational uniform matrix product state (VUMPS) calculations, which work directly in the thermodynamic limit at the cost of a lower accuracy.

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Section: Infinite Systemsmentioning

confidence: 99%

Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

et al. 2023

Self Cite

View full text Add to dashboard Cite

show abstract

“…If U(1) symmetries are exploited in the infinite system, there is to the best of our knowledge no practical way to compute the value of S tot /L. In order to access S tot /L, we switch off the symmetry altogether [48]. Within the degenerate set of 2S tot + 1 states, the DMRG tends to converge to the state with M tot = S tot whose entanglement is minimal.…”

Section: B Infinite Systemsmentioning

confidence: 99%

Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

Rausch¹,

Peschke²,

Plorin³

et al. 2022

Preprint

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The ferrimagnetic phase of the sawtooth chain with mixed ferromagnetic nearest-neighbour interactions J and antiferromagnetic next-nearest-neighbour interactions J (within the isotropic Heisenberg model) was previously characterized as a phase with commensurate order. In this paper, we demonstrate that the system in fact exhibits an incommensurate quantum spin spiral. Even though the ground state is translationally invariant in terms of the local spin expectations Si , the spiral can be detected via the connected spin-spin correlations Si • Sj − Si • Sj between the apical spins. It has a long wavelength that grows with J and that soon exceeds finite-system sizes typically employed in numerical simulations. A faithful treatment thus requires the use of state-of-the-art simulations for large, periodic systems.In this work, we are able to accurately treat L = 400 sites (200 unit cells) with periodic boundary conditions using the density-matrix renormaliztion group (DMRG). This is possible due to the exploitation of the SU(2) symmetry which results in effective bond dimensions of more than 1,000,000. Our results are corroborated by variational uniform matrix product state (VUMPS) calculations, which work directly in the thermodynamic limit at the cost of a lower accuracy.

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“…Furthermore, pair hopping is in principle present as a specific Coulomb interaction term between adjacent atoms [48]. When it enters into a competition with a single-particle hopping term which can destroy the pairs, interesting phases can appear [49]. A coupling of a magnetic impurity to superconducting grains can also break the pairs [17].…”

Section: The Modelmentioning

confidence: 99%

The nuclear many-body problem for large, many-shell nuclei: An exact solution using tensor networks

Rausch,

Plorin,

Peschke

et al. 2021

Preprint

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We introduce an exact numerical technique to solve the nuclear pairing Hamiltonian and to determine properties such as the even-odd mass differences or spectral functions for any element within the periodic table for any number of nuclear shells. In particular, we show that the nucleus is a system with small entanglement and can thus be described efficiently using a one-dimensional tensor network (matrix-product state) despite the presence of long-range interactions. Our approach is numerically cheap and accurate to essentially machine precision, even for large nuclei.We apply this framework to compute the even-odd mass differences of all known lead isotopes from 178 Pb to 220 Pb in the very large configuration space of 13 shells between the neutron magic numbers 82 and 184 (i.e., two major shells) and find good agreement with the experiment. To go beyond the ground state, we calculate the two-neutron removal spectral function of 210 Pb which relates to a two-neutron pickup experiment that probes neutron-pair excitations across the gap of 208 Pb. Finally, we discuss the capabilities of our method to treat pairing with non-zero angular momentum. This is numerically more demanding, but one can still determine the lowest excited states in the full configuration space of one major shell with modest effort, which we demonstrate for the N = 126, Z ≥ 82 isotones.

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Topological phases arising from attractive interaction and pair hopping in the extended Hubbard model

Cited by 7 publications

References 46 publications

Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

The nuclear many-body problem for large, many-shell nuclei: An exact solution using tensor networks

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