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arXiv:1808.02715 · Physical review. B./Physical review. B

Fermionic phases and their transitions induced by competing finite-range interactions

Marcin Szyniszewski, Henning Schomerus

Published Aug 22, 2018• 3 citations
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Abstract

We identify ground states of one-dimensional fermionic systems subject to competing repulsive interactions of finite range, and provide phenomenological and fundamental signatures of these phases and their transitions. Commensurable particle densities admit multiple competing charge-ordered insulating states with various periodicities and internal structure. Our reference point are systems with interaction range $p=2$, where phase transitions between these charge-ordered configurations are known to be mediated by liquid and bond-ordered phases. For increased interaction range $p=4$, we find that the phase transitions can also appear to be abrupt, as well as being mediated by re-emergent ordered phases that cross over into liquid behavior. These considerations are underpinned by a classification of the competing charge-ordered states in the atomic limit for varying interaction range at the principal commensurable particle densities. We also consider the effects of disorder, leading to fragmentization of the ordered phases and localization of the liquid phases.

DOI
10.1103/physrevb.98.075139

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We identify ground states of one-dimensional fermionic systems subject to competing repulsive interactions of finite range, and provide phenomenological and fundamental signatures of these phases and their transitions. Commensurable particle densities admit multiple competing charge-ordered insulating states with various periodicities and internal structure. Our reference point are systems with interaction range p=2p=2p=2, where phase transitions between these charge-ordered configurations are known to be mediated by liquid and bond-ordered phases. For increased interaction range p=4p=4p=4, we find that the phase transitions can also appear to be abrupt, as well as being mediated by re-emergent ordered phases that cross over into liquid behavior. These considerations are underpinned by a classification of the competing charge-ordered states in the atomic limit for varying interaction range at the principal commensurable particle densities. We also consider the effects of disorder, leading to fragmentization of the ordered phases and localization of the liquid phases.
Novel competing orders are found in spin-3/2 cold atomic systems in one-dimensional optical traps and lattices. In particular, the quartetting phase, a four-fermion counterpart of Cooper pairing, exists in a large portion of the phase diagram. The transition between the quartetting and singlet Cooper pairing phases is controlled by an Ising symmetry breaking in one of the spin channels. The singlet Cooper pairing phase also survives in the purely repulsive interaction regime. In addition, various charge and bond ordered phases are identified at commensurate fillings in lattice systems.
In the past few decades, tremendous efforts have been made toward understanding the exotic physics emerging from competition between various ordering tendencies in strongly correlated systems. Employing state-of-the-art quantum Monte Carlo simulation, we investigate an interacting SU(N) fermionic model with varying interaction strength and value of N, and we unveil the ground-state phase diagram of the model exhibiting a plethora of exotic phases. For small values of N-namely, N=2, 3-the ground state is an antiferromagnetic (AFM) phase, whereas in the large-N limit, a staggered valence bond solid (VBS) order is dominant. For intermediate values of N such as N=4, 5, remarkably, our study reveals that distinct VBS orders appear in the weak and strong coupling regimes. More fantastically, the competition between staggered and columnar VBS ordering tendencies gives rise to a Mott insulating phase without spontaneous symmetry breaking (SSB), existing in a large interacting parameter regime, which is consistent with a gapped quantum spin liquid. Our study not only provides a platform to investigate the fundamental physics of quantum many-body systems-it also offers a novel route toward searching for exotic states of matter such as quantum spin liquid in realistic quantum materials.
We study fermions on a finite chain, interacting repulsively when residing on the same and on nearest-neighbor sites, and subjected to a Wannier-Stark linearly varying potential. Using the density matrix renormalization-group numerical technique to solve this generalized extended Hubbard model, the ground state exhibits a staircase of (quasi) plateaus in the average local site density along the chain, decreasing from being doubly filled to empty as the potential increases. These ``plateaus'' represent locked-in commensurate phases of charge density waves together with band and Mott insulators. These phases are separated by incompressible regions with incommensurate fillings. These results differ from the many-body localization proposed for this model earlier. It is suggested that experimental variations of the slope of the potential and the range of the repulsive interactions will produce such a coexistence of phases which have been individually expected theoretically and observed experimentally for uniform systems.
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Predicting the phase diagram of interacting quantum many-body systems is a challenging problem in condensed matter physics. Strong interactions and correlation effects may lead to exotic states of matter, such as quantum spin liquids and unconventional superconductors, that often compete with other symmetry-broken states including ordered magnets and charge density waves. Here, we put forward a formalism for determining the phase diagram of fermionic systems that combines recent progress in the field of Lee-Yang theory of phase transitions with many-body tensor-network methods. Using this strategy, we map out the phase diagram of a fermionic chain, where charge density waves form owing to strong repulsion. Specifically, from the high cumulants of the order parameter, we extract the dominant zeros of the moment-generating function in chains of finite size. By extrapolating their positions to the thermodynamic limit, we determine the boundaries between competing phases. Our formalism provides a strategy for determining critical points in fermionic systems, and it is based on fluctuations of the order parameter, which are measurable quantities.
We study ground state properties and particle excitation spectra across a commensurate charge density wave transition in a system of strongly interacting fermions, using series expansion methods and mean-field theory. We consider a 1/3-filled system of spinless fermions on a triangular lattice, with hopping parameter ttt, nearest-neighbor repulsion VVV, and a sublattice dependent chemical potential ${\ensuremath{\mu}}_{s}$. The phase transition is found to be first order for ${\ensuremath{\mu}}_{s}=0$, but becomes continuous with increasing ${\ensuremath{\mu}}_{s}$. The particle and hole excitation spectra exhibit dramatic changes in the vicinity of the phase transitions and in the charge density wave ordered phase. We discuss the relevance of this study to the pinball Fermi liquid phase postulated theoretically in earlier studies as well as to various strongly correlated triangular lattice materials.