arXiv subjects

Xu-Dong Dai

Publications and source records attributed to Xu-Dong Dai.

6 recordsLinked to original sources

arXiv2026

Topologically Ordered Steady States in Open Quantum Systems

The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a generalization of the ground-state topological degeneracy of closed systems. Specifically, we construct two representative Liouvillians using engineered dissipation, and exactly solve the steady states with topological degeneracy. We find that while the steady-state topological degeneracy is fragile under noise in two dimensions, it is stable in three dimensions, where a genuine many-body phase with topological degeneracy is realized. We identify universal features of steady-state topological physics such as the deconfined emergent gauge field and slow relaxation dynamics of topological defects. The transition from a topologically ordered phase to a trivial phase is also investigated via numerical simulation. Our work highlights the essential difference between ground-state topological order in closed systems and steady-state topological order in open systems.

quant-ph↗

arXiv2026

Scattering-state theory of open Floquet lattices: transfer matrices, branch openness, and robust asymmetry

We establish a scattering-state theory for open one-dimensional Floquet lattices based on a frequency-domain transfer-matrix formulation. For real quasienergy, the conjugate-symplectic structure of the transfer matrix separates bulk Floquet--Bloch modes into propagating and evanescent sectors, enabling a consistent treatment of interface matching and the shrinking-window smoothing required for long-sample transport. By tracking how incoming states populate deep-bulk propagating branches, we define branch-resolved weights $p_{μα}$ and total branch weights $p_μ$. We prove that $p_μ$ equals the escape probability of a wave packet initialized on the corresponding branch. In the open geometries considered here, true bound trapping of propagating branches is nongeneric, yielding $p_μ=1$ for generic parameters. This generic openness implies that long-sample transport is governed by deep-bulk branch populations rather than by boundary-sensitive interference. Consequently, the integrated left--right transmission asymmetry reduces to the net chirality, and hence the winding contribution, of an isolated Floquet band. The robust topological observable is therefore the accumulated asymmetry plateau, not the detailed transmission line shape, which remains strongly reshaped by nonadiabatic boundaries. A spatially adiabatic boundary serves only as a transparent benchmark for resolving the branch structure, not as the origin of the topological response.

cond-mat.mes-hall↗

arXiv2026

Boundary-Robust Transmission Asymmetry as a Topological Signature in Open Floquet Lattices

We identify a boundary-robust topological signature of open Floquet lattices: although nonadiabatic boundaries strongly reshape the transmission lineshape, the integrated left--right transmission asymmetry saturates to a plateau set by the bulk Floquet winding number. Its origin is a deep-bulk branch-population principle: in the long-sample limit, each propagating Floquet--Bloch branch is generically populated with unit weight, since true Floquet bound states are nongeneric. The robust observable is therefore the cumulative transmission imbalance rather than the boundary-sensitive transmission profile. We propose direct detection by cold-atom transmission spectroscopy. For electronic transport, the same asymmetry admits contact-model-dependent electrical readouts: a coherent Floquet--Landauer--Büttiker interpretation predicts a near-$2ef$ response in weak SAW devices, whereas a blocking-factor post-processing yields a qualitatively different signal.

cond-mat.mes-hall↗

arXiv2026

Revisiting Nishimori multicriticality through the lens of information measures

The quantum error correction threshold is closely related to the Nishimori physics of random statistical models. We extend quantum information measures such as coherent information beyond the Nishimori line and establish them as sharp indicators of phase transitions over the full $p$-$T$ plane. These generalized measures admit a natural operational interpretation as diagnostics of inference mismatch for decoders operating at an effective temperature. We derive exact inequalities for several generalized measures, demonstrating that each attains its extremum along the Nishimori line. As a direct application, we study these measures in the 2d $\pm J$ random-bond Ising model-corresponding to a surface code under bit-flip noise-and revisit the Nishimori multicritical point. Among all indicators, coherent information exhibits the weakest finite-size effects, enabling a high-precision estimate $p_c=0.1092212(4)$ and the associated critical exponents.

cond-mat.stat-mech↗

arXiv2023

Steady-state topological order

We investigate a generalization of topological order from closed systems to open systems, for which the steady states take the place of ground states. We construct typical lattice models with steady-state topological order, and characterize them by complementary approaches based on topological degeneracy of steady states, topological entropy, and dissipative gauge theory. Whereas the (Liouvillian) level splitting between topologically degenerate steady states is exponentially small with respect to the system size, the Liouvillian gap between the steady states and the rest of the spectrum decays algebraically as the system size grows, and closes in the thermodynamic limit. It is shown that steady-state topological order remains definable in the presence of (Liouvillian) gapless modes. The topological phase transition to the trivial phase, where the topological degeneracy is lifted, is accompanied by gapping out the gapless modes. Our work offers a toolbox for investigating open-system topology of steady states.

quant-ph↗

arXiv2023

Solvable BCS-Hubbard Liouvillians in arbitrary dimensions

We present the construction of a solvable Lindblad model in arbitrary dimensions, wherein the Liouvillian can be mapped to a BCS-Hubbard model featuring an imaginary interaction. The Hilbert space of the system can be divided into multiple sectors, each characterized by an onsite invariant configuration. The model exhibits bistable steady states in all spatial dimensions, which is guaranteed by the fermion-number parity. Notably, the Liouvillian gap exhibits a Zeno transition, below which the Liouvillian gap is linear with respect to the dissipation. We also uncover a generic dimension-dependent gap behavior: In one dimension, the gap originates from multiple sectors with spectral crossing; in higher dimensions, a single sector determines the gap.

quant-ph↗