arXiv subjects

Yuchi He

Publications and source records attributed to Yuchi He.

16 recordsLinked to original sources

arXiv2026

Lowering the temperature of two-dimensional fermionic tensor networks with cluster expansions

Representing the time-evolution operator as a tensor network constitutes a key ingredient in several algorithms for studying quantum lattice systems at finite temperature or in a non-equilibrium setting. For a Hamiltonian composed of strictly short-ranged interactions, the Suzuki-Trotter decomposition is the main technique for obtaining such a representation. In [B.~Vanhecke, L.~Vanderstraeten and F.~Verstraete, Physical Review A, L020402 (2021)], an alternative strategy, the cluster expansion, was introduced. This approach naturally preserves internal and lattice symmetries and can more easily be extended to higher-order representations or longer-ranged interactions. We extend the cluster expansion to two-dimensional fermionic systems, and employ it to construct projected entangled-pair operator (PEPO) approximations of Gibbs states. We also discuss and benchmark different truncation schemes for multiplying layers of PEPOs together. Applying the resulting framework to a two-dimensional spinless fermion model with attractive interactions, we resolve a clear phase boundary at finite temperature.

cond-mat.str-el↗

arXiv2025

Topological and Trivial Valence-Bond Orders in Higher-Spin Kitaev Models

We investigate the quantum phases of higher-spin Kitaev models using tensor network methods. Our results reveal distinct bond-ordered phases for spin-1, spin-$\tfrac{3}{2}$, and spin-2 models. In all cases, we find translational symmetry breaking with unit cells being tripled by forming valence-bond orders. However, these three phases are distinct, forming plaquette order, topological dimer order, and non-topological dimer order, respectively. Our findings are based on a cross-validation between variational two-dimensional tensor network calculations: an unrestricted exploration of symmetry-broken states versus the detection of symmetry breaking from cat-state behavior in symmetry-restricted states. The origin of different orders can also be understood from a theoretical analysis. Our work sheds light upon the interplay between topological and symmetry-breaking orders as well as their detection via tensor networks.

cond-mat.str-el↗

arXiv2025

Fractional Chern Insulators and Competing States in a Twisted MoTe$_2$ Lattice Model

We construct an interacting lattice model for twisted $\mathrm{MoTe}_{2}$ bilayers at a twist angle of approximately 3.7\degree. We use the infinite density matrix renormalization group (iDMRG) in a cylinder geometry to identify a variety of competing integer and fractional Chern insulators and charge density wave (CDW) states that emerge upon the spontaneous breaking of time reversal symmetry by valley polarization. We use finite-size analysis to establish the robustness of Chern insulating states even in geometries that admit competing CDWs, and explore the phase transitions between these states driven by increasing sublattice potential or interaction strength. Our work highlights the crucial role played by direct spin exchange in stabilizing the parent valley-polarized Chern ferromagnet band, and by the mixing with higher bands in destabilizing CIs/FCIs in favor of CDW orders.

cond-mat.str-el↗

arXiv2024

Kinetic Energy Driven Ferromagnetic Insulator

We construct a minimal model of interacting fermions establishing a ferromagnetic insulating phase. It is based on the Hubbard model on a trimerized triangular lattice in the regime of $t\gg |t^\prime|>0$ with $t$ and $t^\prime$ the intra- and inter-trimer hopping amplitudes, respectively. At the $\frac{1}{3}$-filling, each trimer becomes a triplet spin-1 moment, and the inter-trimer superexchange is ferromagnetic with $J =- \frac{2}{27}\frac{t^{\prime 2}}{t}$ in the limit of $U/t=+\infty$. As $U/t$ becomes finite, the antiferromagnetic superexchange competes with the ferromagnetic one. The system enters into a frustrated antiferromagnetic insulator when $\lambda >U/t\gg 1$ where $\lambda$ is a constant at the order of 10. In contrast, a similar analysis to the trimerized Kagome lattice shows that only the antiferromagnetic superexchange exists at $\frac{1}{3}$-filling.

cond-mat.str-el↗

arXiv2023

Itinerant magnetism in the triangular lattice Hubbard model at half-doping: Application to twisted transition-metal dichalcogenides

We use unrestricted Hartree-Fock, density matrix renormalization group, and variational projected entangled pair state calculations to investigate the ground state phase diagram of the triangular lattice Hubbard model at "half doping" relative to single occupancy, i.e. at a filling of $(1\pm \frac{1}{2})$ electrons per site. The electron-doped case has a nested Fermi surface in the non-interacting limit, and hence a weak-coupling instability towards density-wave orders whose wavevectors are determined by Fermi surface nesting conditions. We find that at moderate to strong interaction strengths other spatially-modulated orders arise, with wavevectors distinct from the nesting vectors. In particular, we identify a series closely-competing itinerant long-wavelength magnetically ordered states, yielding to uniform ferromagnetic order at the largest interaction strengths. For half-hole doping and a similar range of interaction strengths, our data indicate that magnetic orders are most likely absent.

cond-mat.str-el↗

arXiv2023

Electrons interacting with Goldstone modes and the rotating frame

We consider electronic systems with a spontaneously broken continuous symmetry. The scattering vertex between electrons and Goldstone modes is calculated over the entire Brillouin zone using the random phase approximation. This calculation reveals two things: (1) electrons always couple to both $\phi$ and $\partial_t \phi$, where $\phi$ is the Goldstone field, and (2) quasi-particles in a state with continuous symmetry breaking have to be defined in a rotating frame, which locally follows the fluctuations of the order parameter. The implications of these findings for electron spectral functions in both symmetry-broken and thermally disordered systems are discussed, and the examples of anti-ferromagnetism in the Hubbard model and spin spiral order in the three-band model are worked out in detail.

cond-mat.str-el↗

arXiv2023

Fractional Chern Insulator in Twisted Bilayer MoTe$_2$

A recent experiment has reported the first observation of a zero-field fractional Chern insulator (FCI) phase in twisted bilayer MoTe$_2$ moir\'e superlattices [Nature 622, 63-68 (2023)]. The experimental observation is at an unexpected large twist angle 3.7$^\circ$ and calls for a better understanding of the FCI in real materials. In this work, we perform large-scale density functional theory calculation for the twisted bilayer MoTe$_2$, and find that lattice reconstruction is crucial for the appearance of an isolated flat Chern band. The existence of the FCI state at $\nu = -2/3$ are confirmed by exact diagonalization. We establish phase diagrams with respect to the twist angle and electron interaction, which reveal an optimal twist angle of $3.5^\circ$ for the observation of FCI. We further demonstrate that an external electric field can destroy the FCI state by changing band geometry and show evidence of the $\nu=-3/5$ FCI state in this system. Our research highlights the importance of accurate single particle band structure in the quest for strong correlated electronic states and provides insights into engineering fractional Chern insulator in moir\'e superlattices.

cond-mat.str-el↗

arXiv2023

Terminable Transitions in a Topological Fermionic Ladder

Interacting fermionic ladders are important platforms to study quantum phases of matter, such as different types of Mott insulators. In particular, the D-Mott and S-Mott states hold pre-formed fermion pairs and become paired-fermion liquids upon doping (d-wave and s-wave, respectively). We show that the D-Mott and S-Mott phases are in fact two facets of the same topological phase and that the transition between them is terminable. These results provide a quantum analog of the well-known terminable liquid-to-gas transition. However, the phenomenology we uncover is even richer, as in contrast to the former, the order of the transition can be tuned by the interactions from continuous to first-order. The findings are based on numerical results using the variational uniform matrix-product state (VUMPS) formalism for infinite systems, and the density-matrix renormalization group (DMRG) algorithm for finite systems. This is complemented by analytical field-theoretical explanations. In particular, we present an effective theory to explain the change of transition order, which is potentially applicable to a broad range of other systems. The role of symmetries and edge states are briefly discussed.

cond-mat.str-el↗

arXiv2022

Superconductivity of repulsive spinless fermions with sublattice potentials

We explore unconventional superconductivity of repulsive spinless fermions on square and honeycomb lattices with staggered sublattice potentials. The two lattices can exhibit staggered $d$-wave and $f$-wave pairing, respectively, at low doping stemming from an effective two-valley band structure. At higher doping, in particular, the square lattice displays a much richer phase diagram including topological $p+ip$ superconductivity which is induced by a qualitatively different mechanism compared to the $d$-wave pairing. We illuminate this from several complementary perspectives: We analytically perform sublattice projection to analyze the effective continuum low-energy description and we numerically calculate the binding energies for pair and larger bound states for few-body doping near half filling. Furthermore, for finite doping, we present phase diagrams based on extensive functional renormalization group and and density matrix renormalization group calculations.

cond-mat.supr-con↗

arXiv2021

Conductance of correlated many-fermion systems from charge fluctuations

We put forward a relation between the static charge fluctuations and the conductance of correlated many-fermion systems at zero temperature, avoiding the use of time-dependent fluctuations as in the fluctuation-dissipation theorem. Static charge fluctuations can efficiently be computed for low-dimensional systems using tensor network approaches, while the conductance is often significantly more difficult to obtain, requiring a challenging low-frequency linear response computation or an explicit time evolution. We put this relation to the test for quantum dot and quantum point contact setups, where in limiting cases exact results are known. Our study includes systems in which the one-dimensional reservoirs are interacting.

cond-mat.str-el↗

arXiv2021

TMDs as a platform for spin liquid physics: A strong coupling study of twisted bilayer WSe$_2$

The advent of twisted moir\'e heterostructures as a playground for strongly correlated electron physics has led to a plethora of experimental and theoretical efforts seeking to unravel the nature of the emergent superconducting and insulating states. Amongst these layered compositions of two dimensional materials, transition metal dichalcogenides (TMDs) are by now appreciated as highly-tunable platforms to simulate reinforced electronic interactions in the presence of low-energy bands with almost negligible bandwidth. Here, we focus on the twisted homobilayer WSe$_2$ and the insulating phase at half-filling of the flat bands reported therein. More specifically, we explore the possibility of realizing quantum spin liquid (QSL) physics on the basis of a strong coupling description, including up to second nearest neighbor Heisenberg couplings $J_1$ and $J_2$, as well as Dzyaloshinskii-Moriya (DM) interactions. Mapping out the global phase diagram as a function of an out-of-plane displacement field, we indeed find evidence for putative QSL states, albeit only close to SU$(2)$ symmetric points. In the presence of finite DM couplings and XXZ anisotropy, long-range order is predominantly present, with a mix of both commensurate and incommensurate magnetic phases.

cond-mat.str-el↗

arXiv2021

One-dimensional repulsive Hubbard model with mass imbalance: Orders and filling anomaly

We investigate the phase diagram of the one-dimensional repulsive Hubbard model with mass imbalance. Using DMRG, we show that this model has a "triplet" paired phase (dubbed $\pi \mathrm{SG}$) at generic fillings, consistent with previous theoretical analysis. We study the topological aspect of $\pi \mathrm{SG}$ phase, determining long-range string orders and the filling anomaly which refers to the relation among the single particle gap, inversion symmetry, and filling imbalance for open chains. We also find, using DMRG, that at $1/3$ filling, commensurate effects lead to two additional phases: a crystal phase and a trion phase; we construct a description of these phases using Tomonaga-Luttinger liquid theory.

cond-mat.str-el↗

arXiv2020

Charge density waves and their transitions in anisotropic quantum Hall systems

In recent experiments, external anisotropy has been a useful tool to tune different phases and study their competitions. In this paper, we look at the quantum Hall charge density wave states in the $N=2$ Landau level. Without anisotropy, there are two first-order phase transitions between the Wigner crystal, the $2$-electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the $2$-electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that may be observed experimentally is unveiled after the bubble phase gets out. Upon increase of the anisotropy, the energy of the phases at the transitions becomes progressively smooth as a function of the filling. We conclude that all first-order phase transitions are replaced by continuous phase transitions, providing a possible realisation of continuous quantum crystalline phase transitions.

cond-mat.str-el↗

arXiv2019

Pascal conductance series in ballistic one-dimensional LaAlO$_3$/SrTiO$_3$ channels

The ability to create and investigate composite fermionic phases opens new avenues for the investigation of strongly correlated quantum matter. We report the experimental observation of a series of quantized conductance steps within strongly interacting electron waveguides formed at the LaAlO$_3$/SrTiO$_3$ interface. The waveguide conductance follows a characteristic sequence within Pascal's triangle: $(1, 3, 6, 10, 15, ...)\cdot e^2/h$, where $e$ is the electron charge and $h$ is the Planck constant. The robustness of these steps with respect to magnetic field and gate voltage indicate the formation of a new family of degenerate quantum liquids formed from bound states of $n = 2, 3, 4, ...$ electrons. These experiments could provide solid-state analogues for a wide range of composite fermionic phases ranging from neutron stars to solid-state materials to quark-gluon plasmas.

cond-mat.str-el↗

arXiv2018

Emergent mode and bound states in single-component one-dimensional lattice fermionic systems

We study the formation of bound states in a one-dimensional, single-component Fermi chain with attractive interactions. The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of fermion triplets (trion phase), but also a phase with two gapless modes. We show that the latter phase is described by a 2-component Tomonaga-Luttinger liquid (TLL) theory, consisting of one charged and one neutral mode. We argue based on our numerical data, that the single, pair, and trion phases are descendants of the 2-component TLL theory. We speculate on the nature of the phase transitions amongst these phases.

cond-mat.str-el↗

arXiv2016

Entanglement of heterogeneous free fermion chains

We calculate the ground state entanglement entropy between two heterogeneous parts of a free fermion chain. The two parts could be XX chains with different parameters or an XX half chain connected with a quantum Ising half chain. It is shown that logarithmic behavior holds if the two parts are conformally critical. In other cases, area law holds with abundant convergence behaviors. In particular, when XX chain at Lifshitz point is connected with a conformally or Lifshitz critical part, entanglement entropy converges algebraically with a fractional subleading index.

cond-mat.stat-mech↗