Finite-temperature properties of interacting bosons on a two-leg flux ladder

Abstract

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 finitetemperature 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 matrixproduct-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. * Corresponding author: heidrich-meisner@uni-goettingen.deFIG. 1. Meissner and vortex-fluid phase. Ground-state particle current patterns of noninteracting bosons for (a) Meissner phase and (b) vortex-fluid phase. Red arrows indicate the direction and, by their length, the strength of the local currents. The size of the dots and the background shading represent the local particle density. The Hamiltonian parameters φ, J ⊥ , J and U are introduced in Eq.(1). A comprehensive analysis of the Meissner and vortex-fluid phases can be found in, e.g., Refs. [26,[29][30][31][32].fraction of the latter work based on the density-matrix renormalization-group method [33,34], have provided extensive theoretical results regarding the ground-state properties of interacting quantum gases on such ladderlike systems [26,[29][30][31][32]. The presence of gauge fields clearly enriches the corresponding phase diagrams, which by now have been mapped out in large part. For instance, these phase diagrams host superfluid and Mottinsulating vortex-liquid and Meissner phases [29,30,32] and vortex lattices [29,44,46], as well as charge-densitywave [46,48] and biased-ladder phases [40]. Typi-arXiv:1901.07083v3 [cond-mat.quant-gas]

Pretopological fractional excitations in the two-leg flux ladder

“…Several interesting properties have been highlighted by a number of works, for both bosonic [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] and fermionic [53][54][55][56][57][58][59][60][61] flux ladders. Importantly, it was shown that flux ladders, in the quasi-1D limit, can host states that share fundamental properties with 2D FQH states [62][63][64][65], and that can be directly tested in current cold-atom experiments as well as DMRG or MPS simulations [64,65].…”

Interacting bosonic flux ladders with a synthetic dimension: Ground-state phases and quantum quench dynamics

“…exploring the exact parameter regimes that could be accessed in future experiments (including the influence of nearest-neighbor rung-wise interactions, which are typically present in synthetic dimension implementations), investigating the role of finite energy densities and temperatures [40,48,72,77,78] on the ground-state phase diagrams [41], and developing optimal state-preparation and detection protocols (based, for instance, on the dynamics induced by quantum quenches in the flux-ladder model) remain important open questions.…”

Stripes, Antiferromagnetism, and the Pseudogap in the Doped Hubbard Model at Finite Temperature

“…Finite-temperature simulations using DMRG or tensor network techniques beyond ground-state physics were developed early on, but seemed practical mostly for one dimensional systems. The purification method [68,69] is particularly attractive for its simplicity [70][71][72], but in the limit of low temperatures, its representation of the mixed state carries twice the entanglement entropy of the ground state, making it unsuitable for wide ladders, although techniques have been developed to reduce the entanglement growth [73]. The METTS method [66,67] was developed to overcome this obstacle.…”