arXiv subjects

Mingtao Xu

Publications and source records attributed to Mingtao Xu.

6 recordsLinked to original sources

arXiv2026

Spectral Topology and Non-Bloch Band Theory for Domain-Wall Systems

We study the spectral topology of one-dimensional non-Hermitian models in a domain-wall configuration, where different domains are arranged in a ring geometry. While eigenstates can localize near an interface under the non-Hermitian skin effect, we show that the localization of an eigenstate originates from the difference in the spectral winding numbers, with respect to the corresponding eigenenergy, between the two adjacent domains. We then obtain the conditions for the generalized Brillouin zone (GBZ) in the complex momentum space, by extending the Ronkin-function formalism to the domain-wall configuration. In addition to the conventional skin modes that correspond to standing waves on individual domains under the open boundary condition, a unique type of traveling-wave-like skin modes emerges, whose construction involves all domains. Besides their difference in the spatial profiles, these two types of modes obey distinct GBZ conditions, making them differentiable on the GBZ. Interestingly, the traveling-wave-like modes further carry a finite flux spectral winding number, indicating their boundary sensitivity.

cond-mat.mes-hall↗

arXiv2026

Lil: Less is Less When Applying Post-Training Sparse-Attention Algorithms in Long-Decode Stage

Large language models (LLMs) demonstrate strong capabilities across a wide range of complex tasks and are increasingly deployed at scale, placing significant demands on inference efficiency. Prior work typically decomposes inference into prefill and decode stages, with the decode stage dominating total latency. To reduce time and memory complexity in the decode stage, a line of work introduces sparse-attention algorithms. In this paper, we show, both empirically and theoretically, that sparse attention can paradoxically increase end-to-end complexity: information loss often induces significantly longer sequences, a phenomenon we term ``Less is Less'' (Lil). To mitigate the Lil problem, we propose an early-stopping algorithm that detects the threshold where information loss exceeds information gain during sparse decoding. Our early-stopping algorithm reduces token consumption by up to 90% with a marginal accuracy degradation of less than 2% across reasoning-intensive benchmarks.

cs.CL↗

arXiv2026

Higher-order Liouvillian exceptional points in the dissipative dynamics of quadratic fermions

We propose a general class of open fermionic models where quadratic Liouvillians governing the dissipative dynamics feature analytically characterized higher-order exceptional points (EPs). Invoking the formalism of third quantization, we show that, among the multiple EPs of Liouvillian, an EP with its order approaching the system size arises as the dominant modes of the system at long times, leading to a gapless Liouvillian spectrum. By introducing perturbations, in the form of many-body quantum-jump processes, these higher-order EPs break down, leading to finite Liouvillian gaps with fractional power-law scalings. While the power-law scaling is a signature of the higher-order EP, its explicit form is sensitively dependent on the many-body perturbation. Finally, we discuss the long-time dynamics which can serve as detectable signals for the higher-order Liouvillian EPs.

cond-mat.mes-hall↗

arXiv2025

Observation of Non-Hermitian Spectral Deformation in Complex Momentum Space

Open systems feature a variety of phenomena that arise from non-Hermitian physics. Recent theoretical studies have offered much insights into these phenomena through the non-Bloch band theory, though many of the theory's key features are experimentally elusive. For instance, the correspondence between complex momenta and non-Hermitian bands, while central to non-Bloch band theory, has so far defied direct experimental observation. Here we experimentally study the non-Hermitian spectral deformation in complex-momentum space, by implementing a non-Hermitian lattice with long-range couplings in the synthetic orbital-angular-momentum (OAM) dimension of photons inside a degenerate cavity. Encoding the complex momenta in the phase and amplitude modulations of the OAM modes, and devising a complex-momentum-resolved projective detection, we reconstruct the spectral deformation in momentum space, where the eigenspectrum on the complex plane morphs through distinct geometries. This enables us to experimentally extract key information of the system under the non-Bloch band theory, including exceptional points in the complex-momentum space, the open-boundary spectra, and the generalized Brillouin zone. Our work demonstrates a versatile platform for exploring non-Hermitian physics and non-Bloch band theory, and opens the avenue for direct experimental investigation of non-Bloch features in the complex-momentum space.

quant-ph↗

arXiv2025

Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions

In quantum dynamics, the Loschmidt amplitude is analogous to the partition function in the canonical ensemble. Zeros in the partition function indicate a phase transition, while the presence of zeros in the Loschmidt amplitude indicates a dynamical quantum phase transition. Based on the classical-quantum correspondence, we demonstrate that the partition function of a classical Ising model is equivalent to the Loschmidt amplitude in non-Hermitian dynamics, thereby mapping an Ising model with variable system size to the non-Hermitian dynamics. It follows that the Yang-Lee zeros and the Yang-Lee edge singularity of the classical Ising model correspond to the critical times of the dynamic quantum phase transitions and the exceptional point of the non-Hermitian Hamiltonian, respectively. Our work reveals an inner connection between Yang-Lee zeros and non-Hermitian dynamics, offering a dynamic characterization of the former.

quant-ph↗

arXiv2025

Optimal spectral transport of non-Hermitian systems

The optimal transport problem seeks to minimize the total transportation cost between two distributions, thus providing a measure of distance between them. In this work, we study the optimal transport of the eigenspectrum of one-dimensional non-Hermitian models as the spectrum deforms on the complex plane under a varying imaginary gauge field. Notably, according to the non-Bloch band theory, the deforming spectrum continuously connects the eigenspectra of the original non-Hermitian model (with vanishing gauge field) under different boundary conditions. It follows that the optimal spectral transport should contain key information of the model. Characterizing the optimal spectral transport through the Wasserstein metric, we show that, indeed, important features of the non-Hermitian model, such as the (auxiliary) generalized Brillouin zone, the non-Bloch exceptional point, and topological phase transition, can be determined from the Wasserstein-metric calculation. We confirm our conclusions using concrete examples. Our work highlights the key role of spectral geometry in non-Hermitian physics, and offers a practical and convenient access to the properties of non-Hermitian models.

quant-ph↗