Quantum phase transitions of a two-leg bosonic ladder in an artificial gauge field

Abstract

We consider a two leg bosonic ladder in a U (1) gauge field with both interleg hopping and interleg repulsion. As a function of the flux, the interleg interaction converts the commensurateincommensurate transition from the Meissner to a Vortex phase, into an Ising-type of transition towards a density wave phase. A disorder point is also found after which the correlation functions develop a damped sinusoid behavior signaling a melting of the vortex phase. We discuss the differences on the phase diagram for attractive and repulsive interleg interaction. In particular, we show how repulsion favors the Meissner phase at low-flux and a phase with a second incommensuration in the correlation functions for intermediate flux, leading to a richer phase diagram than in the case of interleg attraction. The effect of the temperature on the chiral current is also discussed.

Topological Devil’s staircase in atomic two-leg ladders

“…In the last few years, a series of remarkable experiments has demonstrated how cold atomic gases in optical lattices can realize topological band structures [1][2][3][4][5][6][7] with a high degree of accuracy and tunability [8][9][10][11][12]. In the context of one-dimensional (1D) systems, ladders pierced by synthetic gauge fields [13][14][15][16][17][18][19][20][21][22][23] have been experimentally shown to display a plethora of phenomena, including chiral currents [24] and edge modes akin to the two-dimensional Hall effect [7], accompanied with the long-predicted-but hard to directly observeskipping orbits [25,26]. While such phenomena have required relatively simple microscopic Hamiltonians apt to describe electrons in a magnetic field [27], the flexibility demonstrated in very recent settings utilizing alkaline-earth-like atoms [28][29][30][31][32][33] has shown how a new class of model Hamiltonians-where nearest neighbor couplings on multi-leg ladders can be engineered almost independently one from the other-is well within experimental reach.…”

Spectral Function of a Boson Ladder in an Artificial Gauge Field

“…Previous work has shown [36,51] that it splits the commensurate incommensurate transition point Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 3 February 2020 doi:10.20944/preprints202002.0013.v1…”

Spectral Function of a Boson Ladder in an Artificial Gauge Field

“…Another possible extension is to consider the interleg interaction. Previous work has shown [38,53] that it splits the commensurate-incommensurate transition point into an Ising transition point, a disorder point and a Berezinskii-Kosterltz-Thouless (BKT) transition point. An intermediate atomic density wave exists between the Ising and the BKT point, and it develops incommensuration at the disorder point.…”

“…describes the antisymmetric density (or spin) fluctuations. In Equations (2) and 3, u s and u c are, respectively, the velocity of antisymmetric and total density excitations, A 0 is a non-universal coefficient [21] while K s and K c are the corresponding Tomonaga-Luttinger (TL) exponents [38]. For two chains of hard core bosons, we have u c = u s = 2t sin(πρ 0 /2) where ρ 0 is the average number of bosons per site and K s = K c = 1.…”