Strong-coupling expansion of multi-band interacting models: Mapping onto the transverse-field J1-J2 Ising model
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Strong-coupling expansion of multi-band interacting models : Mapping onto the transverse-field J1-J2 Ising model. / Wang, Xiaoyu; Christensen, Morten H.; Berg, Erez; Fernandes, Rafael M.
I: Annals of Physics, Bind 435, 168522, 12.2021.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Strong-coupling expansion of multi-band interacting models
T2 - Mapping onto the transverse-field J1-J2 Ising model
AU - Wang, Xiaoyu
AU - Christensen, Morten H.
AU - Berg, Erez
AU - Fernandes, Rafael M.
PY - 2021/12
Y1 - 2021/12
N2 - We investigate a class of two-dimensional two-band microscopic models in which the inter-band repulsive interactions play the dominant role. We first demonstrate three different schemes of constraining the ratios between the three types of inter-band interactions - density-density, spin exchange, and pair-hopping that render the model free of the fermionic sign-problem for any filling and, consequently, amenable to efficient Quantum Monte Carlo simulations. We then study the behavior of these signproblem-free models in the strong-coupling regime. In the cases where spin-rotational invariance is preserved or lowered to a planar symmetry, the strong-coupling ground state is a quantum paramagnet. However, in the case where there is only a residual Ising symmetry, the strong-coupling expansion maps onto the transverse-field J(1)-J(2) Ising model, whose pseudospins are associated with local inter-band magnetic order. We show that by varying the band structure parameters within a reasonable range of values, a variety of ground states and quantum critical points can be accessed in the strong-coupling regime, some of which are not realized in the weak-coupling regime. We compare these results with the case of the single-band Hubbard model, where only intra-band repulsion is present, and whose strong-coupling behavior is captured by a simple Heisenberg model. (C) 2021 Elsevier Inc. All rights reserved.
AB - We investigate a class of two-dimensional two-band microscopic models in which the inter-band repulsive interactions play the dominant role. We first demonstrate three different schemes of constraining the ratios between the three types of inter-band interactions - density-density, spin exchange, and pair-hopping that render the model free of the fermionic sign-problem for any filling and, consequently, amenable to efficient Quantum Monte Carlo simulations. We then study the behavior of these signproblem-free models in the strong-coupling regime. In the cases where spin-rotational invariance is preserved or lowered to a planar symmetry, the strong-coupling ground state is a quantum paramagnet. However, in the case where there is only a residual Ising symmetry, the strong-coupling expansion maps onto the transverse-field J(1)-J(2) Ising model, whose pseudospins are associated with local inter-band magnetic order. We show that by varying the band structure parameters within a reasonable range of values, a variety of ground states and quantum critical points can be accessed in the strong-coupling regime, some of which are not realized in the weak-coupling regime. We compare these results with the case of the single-band Hubbard model, where only intra-band repulsion is present, and whose strong-coupling behavior is captured by a simple Heisenberg model. (C) 2021 Elsevier Inc. All rights reserved.
KW - QUANTUM MONTE-CARLO
KW - HUBBARD-MODEL
KW - SUPERCONDUCTIVITY
KW - TRANSITION
KW - ANTIFERROMAGNETISM
KW - RENORMALIZATION
KW - FERROMAGNETISM
KW - INSULATOR
KW - SYMMETRY
KW - LIMIT
U2 - 10.1016/j.aop.2021.168522
DO - 10.1016/j.aop.2021.168522
M3 - Journal article
VL - 435
JO - Annals of Physics
JF - Annals of Physics
SN - 0003-4916
M1 - 168522
ER -
ID: 289167572