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arXiv:2008.00708 · Physical Review A

Synthetic Hall tube of interacting fermions

Xiaofan Zhou, Gang Chen, Suotang Jia

Published Oct 9, 2020• 5 citations
arXivHTMLPDF

Abstract

Motivated by a recent experiment [J. H. Han et al., Phys. Rev. Lett. 122, 065303 (2019)], we investigate the many-body physics of interacting fermions in a synthetic Hall tube, using a state-of-the-art density-matrix renormalization-group numerical method. Since the interleg couplings of this synthetic Hall tube generate an interesting spin-tensor Zeeman field, exotic topological and magnetic properties occur. In particular, four quantum phases, such as nontopological spin-vector and -tensor paramagnetic insulators, and topological and nontopological spin-mixed paramagnetic insulators, are predicted by calculating the entanglement spectrum, entanglement entropies, energy gaps, and local magnetic orders with three spin vectors and five spin tensors. Moreover, the topologically magnetic phase transitions induced by the interaction as well as the interleg couplings are also revealed. Our results establish a way to explore many-body (topological) states induced by both the spiral spin-vector and -tensor Zeeman fields.

DOI
10.1103/physreva.102.043313

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Motivated by a recent experiment [J. H. Han et al., Phys. Rev. Lett. 122, 065303 (2019)], we investigate the many-body physics of interacting fermions in a synthetic Hall tube, using a state-of-the-art density-matrix renormalization-group numerical method. Since the interleg couplings of this synthetic Hall tube generate an interesting spin-tensor Zeeman field, exotic topological and magnetic properties occur. In particular, four quantum phases, such as nontopological spin-vector and -tensor paramagnetic insulators, and topological and nontopological spin-mixed paramagnetic insulators, are predicted by calculating the entanglement spectrum, entanglement entropies, energy gaps, and local magnetic orders with three spin vectors and five spin tensors. Moreover, the topologically magnetic phase transitions induced by the interaction as well as the interleg couplings are also revealed. Our results establish a way to explore many-body (topological) states induced by both the spiral spin-vector and -tensor Zeeman fields.
Exploring topological phases in interacting systems is a challenging task. We investigate many-body topological physics of interacting fermions in an extended Su-Schrieffer-Heeger (SSH) model, which extends the two sublattices of the SSH model into four sublattices and thus is dubbed the SSH4 model, based on the density-matrix renormalization-group numerical method. The interaction-driven phase transition from the topological insulator phase to the charge density wave (CDW) phase can be identified by analyzing the variations of the entanglement spectrum, entanglement entropies, energy gaps, CDW order parameter, and fidelity. We map the global phase diagram of the many-body ground state, which contains nontrivial topological insulator, trivial insulator, and CDW phases, respectively. In contrast to the interacting SSH model, in which the phase transitions to the CDW phase are argued to be first-order phase transitions, the phase transitions between the CDW phase and topologically trivial or nontrivial phases are shown to be continuous phase transitions. Finally, we also show the phase diagram of the interacting spinful SSH4 model, where the attractive (repulsive) on-site spin interaction amplifies (suppresses) the CDW phase. The models analyzed here can be implemented with ultracold atoms on optical superlattices.
An innovative way to produce quantum Hall ribbons in a cold atomic system is to use MMM hyperfine states of atoms in a one-dimensional optical lattice to mimic an additional ``synthetic dimension.'' A notable aspect here is that the SU(MMM) symmetric interaction between atoms manifests as ``infinite ranged'' along the synthetic dimension. We study the many-body physics of fermions with SU(MMM) symmetric attractive interactions in this system using a combination of analytical field theoretic and numerical density-matrix renormalization-group methods. We uncover the rich ground-state phase diagram of the system, including unconventional phases such as squished baryon fluids, shedding light on many-body physics in low dimensions. Remarkably, changing the parameters entails interesting crossovers and transition; e.g., we show that increasing the magnetic field (that produces the Hall effect) converts a ``ferrometallic'' state at low fields to a ``squished baryon superfluid'' (with algebraic pairing correlations) at high fields. We also show that this system provides a unique opportunity to study quantum phase separation in a multiflavor ultracold fermionic system.
Synthetic ladders pierced by a magnetic field realized with one-dimensional alkaline-earth(-like) fermionic gases represent a promising environment for the investigation of quantum-Hall physics with ultracold atoms. We unveil the existence of a hierarchy of insulating and conducting states which appear at fractional filling factors by means of both analytical and numerical methods based on the density-matrix renormalization group algorithm. Analogously to the original quantum Hall effect, we show that such states can be exploited for constructing a topological Thouless pump where the charge transported after one cycle is quantized to fractional values and demonstrate this behavior with a full many-body time-dependent calculation. We conclude with some results on Laughlin-like states in both fermionic and bosonic systems.
We report the experimental realization of a synthetic three-leg Hall tube with ultracold fermionic atoms in a one-dimensional optical lattice. The legs of the synthetic tube are composed of three hyperfine spin states of the atoms, and the cyclic interleg links are generated by two-photon Raman transitions between the spin states, resulting in a uniform gauge flux ϕ penetrating each side plaquette of the tube. Using quench dynamics, we investigate the band structure of the Hall tube system for a commensurate flux ϕ=2π/3. Momentum-resolved analysis of the quench dynamics reveals a critical point of band gap closing as one of the interleg coupling strengths is varied, which is consistent with a topological phase transition predicted for the Hall tube system.
Synthetic ladders realized with one-dimensional alkaline-earth(-like) fermionic gases and subject to a gauge field represent a promising environment for the investigation of quantum Hall physics with ultracold atoms. Using density-matrix renormalization group calculations, we study how the quantum Hall-like chiral edge currents are affected by repulsive atom–atom interactions. We relate the properties of such currents to the asymmetry of the spin resolved momentum distribution function, a quantity which is easily addressable in state-of-art experiments. We show that repulsive interactions significantly enhance the chiral currents. Our numerical simulations are performed for atoms with two and three internal spin states.
The concept of topology in condensed matter physics has led to the discovery of rich and exotic physics in recent years. Especially when strong correlations are included, phenomenons such as fractionalization and anyonic particle statistics can arise. In this thesis, we study several systems hosting topological phases of interacting fermions. In the first part, we consider one-dimensional systems of parafermions, which are generalizations of Majorana fermions, in the presence of a Z_N charge symmetry. We classify the symmetry-protected topological (SPT) phases that can occur in these systems using the projective representations of the symmetries and find a finite number of distinct phases depending on the prime factorization of N. The different phases exhibit characteristic degeneracies in their entanglement spectrum (ES). Apart from these SPT phases, we report the occurrence of parafermion condensate phases for certain values of N. When including an additional Z_N symmetry, we find a non-Abelian group structure under the addition of phases. In the second part of the thesis, we focus on two-dimensional lattice models of spinless fermions. First, we demonstrate the detection of a fractional Chern insulator (FCI) phase in the Haldane honeycomb model on an infinite cylinder by means of the density-matrix renormalization group (DMRG). We report the calculation of several quantities characterizing the topological order of the state, i.e., (i)~the Hall conductivity, (ii)~the spectral flow and level counting in the ES, (iii)~the topological entanglement entropy, and (iv)~the charge and topological spin of the quasiparticles. Since we have access to sufficiently large system sizes without band projection with DMRG, we are in addition able to investigate the transition from a metal to the FCI at small interactions which we find to be of first order. In a further study, we consider a time-reversal symmetric model on the honeycomb lattice where a Chern insulator (CI) induced by next-nearest neighbor interactions has been predicted by mean field theory. However, various subsequent studies challenged this picture and it was still unclear whether the CI would survive quantum fluctuations. We therefore map out the phase diagram of the model as a function of the interactions on an infinite cylinder with DMRG and find evidence for the absence of the CI phase. However, we report the detection of two novel charge-ordered phases and corroborate the existence of the remaining phases that had been predicted in mean field theory. Furthermore, we characterize the transitions between the various phases by studying the behavior of correlation length and entanglement entropy at the phase boundaries. Finally, we develop an improvement to the DMRG algorithm for fermionic lattice models on cylinders. By using a real space representation in the direction along the cylinder and a real space representation in the perpendicular direction, we are able to use the momentum around the cylinder as conserved quantity to reduce computational costs. We benchmark the method by studying the interacting Hofstadter model and report a considerable speedup in computation time and a severely reduced memory usage.