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Register a new userEmergent bosons in the fermionic two-leg flux ladder
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Added by
Marcello Calvanese Strinati
Publication date
2019
fields
Physics
and research's language is
English
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We study the emergence of bosonic pairs in a system of two coupled one-dimensional fermionic chains subject to a gauge flux (two-leg flux ladder), with both attractive and repulsive interaction. In the presence of strong attractive nearest-neighbor interaction and repulsive next-to-nearest-neighbor interaction, the system crosses into a regime in which fermions form tightly bound pairs, which behave as bosonic entities. By means of numerical simulations based on the density-matrix-renormalization-group (DMRG) method, we show in particular that in the strongly paired regime, the gauge flux induces a quantum phase transition of the Ising type from vortex density wave (VDW) to a charge density wave (CDW), characteristic of bosonic systems.
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Topological order, the hallmark of fractional quantum Hall states, is primarily defined in terms of ground-state degeneracy on higher-genus manifolds, e.g. the torus. We investigate analytically and numerically the smooth crossover between this topological regime and the Tao-Thouless thin torus quasi-1D limit. Using the wire-construction approach, we analyze an emergent charge density wave (CDW) signifying the break-down of topological order, and relate its phase shifts to Wilson loop operators. The CDW amplitude decreases exponentially with the torus circumference once it exceeds the transverse correlation length controllable by the inter-wire coupling. By means of numerical simulations based on the matrix product states (MPS) formalism, we explore the extreme quasi-1D limit in a two-leg flux ladder and present a simple recipe for probing fractional charge excitations in the $ u=1/2$ Laughlin-like state of hard-core bosons. We discuss the possibility of realizing this construction in cold-atom experiments. We also address the implications of our findings to the possibility of producing non-Abelian zero modes. As known from rigorous no-go theorems, topological protection for exotic zero modes such as parafermions cannot exist in 1D fermionic systems and the associated degeneracy cannot be robust. Our theory of the 1D-2D crossover allows to calculate the splitting of the degeneracy, which vanishes exponentially with the number of wires, similarly to the CDW amplitude.
Quasi-one-dimensional lattice systems such as flux ladders with artificial gauge fields host rich quantum-phase diagrams that have attracted great interest. However, so far, most of the work on these systems has concentrated on zero-temperature phases while the corresponding finite-temperature regime remains largely unexplored. The question if and up to which temperature characteristic features of the zero-temperature phases persist is relevant in experimental realizations. We investigate a two-leg ladder lattice in a uniform magnetic field and concentrate our study on chiral edge currents and momentum-distribution functions, which are key observables in ultracold quantum-gas experiments. These quantities are computed for hard-core bosons as well as noninteracting bosons and spinless fermions at zero and finite temperatures. We employ a matrix-product-state based purification approach for the simulation of strongly interacting bosons at finite temperatures and analyze finite-size effects. Our main results concern the vortex-fluid-to-Meissner crossover of strongly interacting bosons. We demonstrate that signatures of the vortex-fluid phase can still be detected at elevated temperatures from characteristic finite-momentum maxima in the momentum-distribution functions, while the vortex-fluid phase leaves weaker fingerprints in the local rung currents and the chiral edge current. In order to determine the range of temperatures over which these signatures can be observed, we introduce a suitable measure for the contrast of these maxima. The results are condensed into a finite-temperature crossover diagram for hard-core bosons.
New phases with broken discrete Ising symmetries are uncovered in quantum materials with strong electronic correlations. The two-leg ladder cuprate textbf{$Sr_{14-x}Ca_{x}Cu_{24}O_{41}$} hosts a very rich phase diagram where, upon hole doping, the system exhibits a spin liquid state ending to an intriguing ordered magnetic state at larger $Ca$ content. Using polarized neutron diffraction, we report here the existence of short range magnetism in this material for two $Ca$ contents, whose origin cannot be ascribed to Cu spins. This magnetism develops exclusively within the two-leg ladders with a diffraction pattern at forbidden Bragg scattering which is the hallmark of loop current-like magnetism breaking both time-reversal and parity symmetries. Our discovery shows local discrete symmetry breaking in a one dimensional spin liquid system as theoretically predicted. It further suggests that a loop current-like phase could trigger the long range magnetic order reported at larger doping in two-leg ladder cuprates.
The Hubbard model on a two-leg ladder structure has been studied by a combination of series expansions at T=0 and the density-matrix renormalization group. We report results for the ground state energy $E_0$ and spin-gap $Delta_s$ at half-filling, as well as dispersion curves for one and two-hole excitations. For small $U$ both $E_0$ and $Delta_s$ show a dramatic drop near $t/t_{perp}sim 0.5$, which becomes more gradual for larger $U$. This represents a crossover from a band insulator phase to a strongly correlated spin liquid. The lowest-lying two-hole state rapidly becomes strongly bound as $t/t_{perp}$ increases, indicating the possibility that phase separation may occur. The various features are collected in a phase diagram for the model.
We report on zero-field muon spin rotation, electron spin resonance and polarized Raman scattering measurements of the coupled quantum spin ladder Ba2CuTeO6. Zero-field muon spin rotation and electron spin resonance probes disclose a successive crossover from a paramagnetic through a spin-liquid-like into a magnetically ordered state with decreasing temperature. More significantly, the two-magnon Raman response obeys a T-linear scaling relation in its peak energy, linewidth and intensity. This critical scaling behavior presents an experimental signature of proximity to a quantum critical point from an ordered side in Ba2CuTeO6.
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