We investigate the quantum phases of hard-core bosonic atoms in an extended Hubbard model where particles interact via soft-shoulder potentials in one dimension. Using a combination of field-theoretical methods and strong-coupling perturbation theory, we demonstrate that the low-energy phase can be a conformal cluster Luttinger liquid (CLL) phase with central charge $c=1$, where the microscopic degrees of freedom correspond to mesoscopic ensembles of particles. Using numerical density-matrix-renormalization-group methods, we demonstrate that the CLL phase, first predicted in [Phys. Rev. Lett. 111, 165302 (2013)], is separated from a conventional Tomonaga-Luttinger liquid by an exotic critical point with central charge $c=3/2$. The latter is expression of an emergent conformal supersymmetry, which is not present in the original Hamiltonian. We discuss the observability of the CLL phase in realistic experimental settings with weakly-dressed Rydberg atoms confined to optical lattices. Using quantum Monte-Carlo simulations, we show that the typical features of CLLs are stable up to comparatively high temperatures. Using exact diagonalizations and quantum trajectory methods, we provide a protocol for adiabatic state preparation as well as quantitative estimates on the effects of particle losses.
We investigate the zero-temperature phases of bosonic and fermionic gases confined to one dimension and interacting via a class of finite-range soft-shoulder potentials (i.e. soft-core potentials with an additional hard-core onsite interaction). Using a combination of analytical and numerical methods, we demonstrate the stabilization of critical quantum liquids with qualitatively new features with respect to the Tomonaga-Luttinger liquid paradigm. These features result from frustration and cluster formation in the corresponding classical ground-state. Characteristic signatures of these liquids…
Recent ultracold atomic gas experiments implementing synthetic spin-orbit coupling allow access to flatbands that emphasize interactions. We model spin-orbit coupled fermions in a one-dimensional flatband optical lattice. We introduce an effective Luttinger-liquid theory to show that interactions generate collective excitations with emergent kinetics and fractionalized charge, analogous to properties found in the two-dimensional fractional quantum Hall regime. Observation of these excitations would provide an important platform for exploring exotic quantum states derived solely from interactio…
The emergent phases of strongly correlated spin-1/2 Fermi gases of Rydberg dressed atoms in a one dimensional optical lattice are theoretically investigated. At weak coupling a bosonization description is used to demonstrate the ability to drive alternating quantum phase transitions between distinct Luttinger liquids. At strong coupling the ground state develops non-trivial phase separation exhibiting Luttinger liquid ''puddles'' separated by magnetic domain walls due to the interplay of the incommensurate filling and the Rydberg core length scale. These phases can be detected in ultracold gas…
A Luttinger liquid (LL) describes low energy excitations of many interacting one dimensional systems, and exhibits universal response both in and out of equilibrium. We analyze its behaviour in the non-hermitian realm after quantum quenching to a PT-symmetric LL by focusing on the fermionic single particle density matrix. For short times, we demonstrate the emergence of unique phenomena, characteristic to non-hermitian systems, that correlations propagate faster than the conventional maximal speed, known as the Lieb-Robinson bound. These emergent supersonic modes travel with velocities that ar…
The degenerate Bose-Fermi (BF) mixtures in one dimension present a novel realization of two decoupled Luttinger liquids with bosonic and fermionic degrees of freedom at low temperatures. However, the transport properties of such decoupled Luttinger liquids of charges have not yet been studied. Here we apply generalized hydrodynamics to study the transport properties of one-dimensional (1D) BF mixtures with delta-function interactions. The initial state is set up as the semi-infinite halves of two 1D BF mixtures with different temperatures, joined together at the time $t=0$ and the junction poi…
We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest neighbour range. In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbour and next-nearest-neighbour interactions. Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations. The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably ri…
Emergent superconformal symmetry in the phase diagram of a 1D $\mathbb{Z}_{2}$ lattice gauge theory
Karlstad University（卡尔斯特大学）；Andronikashvili Institute of Physics（安德罗尼卡什维利物理研究所）；Ilia State University（伊利亚州立大学）；Heinrich-Heine-Universität（海因里希·海涅大学）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔，皇家理工学院与斯德哥尔摩大学）
We consider a zero-temperature one-dimensional system of bosons interacting via the soft-shoulder potential in the continuum, typical of dressed Rydberg gases. We employ quantum Monte Carlo simulations, which allow for the exact calculation of imaginary-time correlations, and a stochastic analytic continuation method, to extract the dynamical structure factor. At finite densities, in the weakly-interacting homogeneous regime, a rotonic spectrum marks the tendency to clustering. With strong interactions, we indeed observe cluster liquid phases emerging, characterized by the spectrum of a compos…
We revisit the low energy physics of one dimensional spinless fermion liquids, showing that with sufficiently strong interactions the conventional Luttinger liquid can give way to a strong pairing phase. While the density fluctuations in both phases are described by a gapless Luttinger liquid, single fermion excitations are gapped only in the strong pairing phase. Smooth spatial Interfaces between the two phases lead to topological degeneracies in the ground state and low energy phonon spectrum. Using a concrete microscopic model, with both single particle and pair hopping, we show that the st…
Coupling dynamical charges to gauge fields can result in highly non-local interactions with a linear confining potential. As a consequence, individual particles bind into mesons which, in one dimension, become the new constituents of emergent Luttinger liquids. Furthermore, at commensurate fillings, different Mott-insulating states can be stabilized by including nearest-neighbour (NN) interactions among charges. However, rich phase diagrams expected in such models have not been fully explored and still lack comprehensive theoretical explanation. Here, by combining numerical and analytical tool…
We theoretically study an ultra-cold gas of spin-1 polar bosons in a one dimensional continuum which are subject to linear and quadratic Zeeman fields and a Raman induced spin-orbit coupling. Concentrating on the regime in which the background fields can be treated perturbatively we analytically solve the model in its low-energy sector, i.e. we characterize the relevant phases and the quantum phase transitions between them. Depending on the sign of the effective quadratic Zeeman field $ε$, two superfluid phases with distinct nematic order appear. In addition, we uncover a spin-disordered super…
The realization of experimental platforms exhibiting one dimensional (1D) quantum phenomena has been elusive, due to their inherent lack of stability, with a few notable exceptions including spin chains, carbon nanotubes and ultracold low-density gasses. The difficulty of such systems in exhibiting long range order is integral to their effective description in terms of the Tomonaga-Luttinger liquid theory. Recently, it has been proposed that bosonic superfluid 4He could realize a 1D quantum system beyond the Luttinger liquid paradigm. Here we describe an experimental observation of this behavi…
We show that a one dimensional ultra-cold Fermi gas with Rashba-like spin orbit coupling, a Zeeman field and intrinsic attractive interactions exhibits a novel topological superfluid state, which forms in spite of total number conservation and the absence of a single particle gap. Majorana zero modes are localized to the interface between a topological region in the middle of the trap and trivial regions at its wings. Unlike the realization of a topological superconductor in proximity coupled nano-wires, the Majorana modes do not carry a quantum number associated with the total fermion parity.…
We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical $Z_2$ gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the Density Matrix Renormalization Group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excita…
The recent experimental condensation of ultracold atoms in a triangular optical lattice with negative effective tunneling energies paves the way to study frustrated systems in a controlled environment. Here, we explore the critical behavior of the chiral phase transition in such a frustrated lattice in three dimensions. We represent the low-energy action of the lattice system as a two-component Bose gas corresponding to the two minima of the dispersion. The contact repulsion between the bosons separates into intra- and inter-component interactions, referred to as $V_{0}$ and $V_{12}$, respecti…
