arXiv subjects

Xueda Wen

Publications and source records attributed to Xueda Wen.

At least 19 recordsLinked to original sources

arXiv2026

Exactly solvable non-unitary conformal interfaces in unitary CFTs

We construct directly on the lattice a class of non-unitary interfaces that are both exactly conformal and exactly solvable, and establish their corresponding boundary and interface conformal field theory (CFT) descriptions. The construction is obtained by analytically continuing the scattering data of known exact unitary conformal interfaces on the lattice, yielding an $SL(2,\mathbb C)$-parametrized family, which is non-compact and breaks probability-current conservation. Exploiting the exact lattice-continuum correspondence, we derive the conformal boundary states in the folded picture. We show that a proper definition of the Hilbert space in the closed-string channel requires the incoming and outgoing boundary states to be specified independently by boundary data associated with a pair of dual biorthogonal bases, in close analogy with the right and left eigenvectors of a non-Hermitian Hamiltonian. This requirement determines a consistent CFT construction of non-unitary boundaries and interfaces, and leads to a non-unitary generalization of the conventional Cardy's condition for unitary boundary CFT. Beyond their formal construction, these non-unitary interfaces are shown to exhibit logarithmic entanglement scaling governed by an effective central charge that is generally complex. For the $SU(1,1)$ subclass, the effective central charge remains real but grows without bound as the transmission coefficient increases. This result is demonstrated through analytical and numerical lattice calculations, as well as an interface CFT analysis in the unfolded picture. Finally, we present a general CFT analysis of a class of global quantum quenches whose initial states are prepared with non-unitary boundaries. We relate their effective temperature to the conformal dimension of the boundary-condition-changing operators associated with non-unitary boundary conditions.

cond-mat.stat-mech↗

arXiv2026

Exact operator dynamics in Lindbladian Wess-Zumino-Witten conformal field theories

Understanding the time evolution of physical observables in open quantum many-body systems coupled to external environments is a natural and difficult problem, and exact results are still rare. In this work, we study this problem for Wess-Zumino-Witten (WZW) conformal field theories with Lindblad jump operators linear in Kac-Moody current modes. We investigate the exact operator dynamics generated by these Lindbladians, identifying classes of current operators whose Heisenberg equations close and can therefore be solved analytically using the underlying current algebra. In Abelian $U(1)_k$ WZW theories, this closure of operator dynamics holds for arbitrary settings of jump rates and includes exactly tractable cooling dynamics. In contrast, for non-Abelian WZW theories, exact closure occurs only for symmetric current-mode dissipation, where upward and downward current-mode transitions occur with equal rates, and even then it leads to a simple closed evolution only for a single current operator. Generic imbalances, including those needed for cooling, produce additional non-Abelian terms and prevent closure of the opeartor dynamics. Consequently, the current algebra gives rise to a broad family of exactly solvable dissipative dynamics in the Abelian setting, whereas in the non-Abelian case it singles out only a special exactly solvable dynamics corresponding to an infinite-temperature bath.

cond-mat.stat-mech↗

arXiv2026

Detecting Higher Berry Phase via Boundary Scattering

Higher Berry phase has recently been proposed to study the topology of the space of gapped many-body quantum systems. In this work, we develop a boundary-scattering approach to detect higher Berry phases in one-dimensional gapped free-fermion systems. By coupling a gapless lead to the gapped system, we demonstrate that the higher Berry invariant can be obtained by studying the higher winding number of the boundary reflection matrix. The resulting topological invariant is robust against perturbations such as disorder. Our approach establishes a connection between higher Berry invariants and transport properties, thereby providing a potentially experimentally accessible probe of parametrized topological phases.

cond-mat.str-el↗

arXiv2026

Dissipation meets conformal interface in open quantum systems: How the relaxation rate is suppressed

Conformal interfaces play an important role in quantum critical systems. In closed systems, the transmission properties of conformal interfaces are typically characterized by two quantities: One is the effective central charge $c_{\text{eff}}$, which measures the amount of quantum entanglement through the interface, and the other is the transmission coefficient $c_{\text{LR}}$, which measures the energy transmission through the interface. In the present work, to characterize the transmission property of conformal interfaces in open quantum systems, we propose a third quantity $c_{\text{relax}}$, which is defined through the ratio of Liouvillian gaps with and without an interface. Physically, $c_{\text{relax}}$ measures the suppression of the relaxation rate towards a steady state when the system is subject to a local dissipation. We perform both analytical perturbation calculations and exact numerical calculations based on a free fermion chain at the critical point. It is found that $c_{\text{relax}}$ decreases monotonically with the strength of the interface. In particular, $0\le c_{\text{relax}}\le c_{\text{LR}}\le c_{\text{eff}}$, where the equalities hold if and only if the interface is totally reflective or totally transmissive. Our result for $c_{\text{relax}}$ is universal in the sense that $c_{\text{relax}}$ is independent of (i) the dissipation strength in the weak dissipation regime and (ii) the location where the local dissipation is introduced. Comparing to the previously known $c_{\text{LR}}$ and $c_{\text{eff}}$ in a closed system, our $c_{\text{relax}}$ shows a distinct behavior as a function of the interface strength, suggesting its novelty to characterize conformal interfaces in open systems and offering insights into critical systems under dissipation.

cond-mat.str-el↗

arXiv2026

Relaxation Process During Complex Time Evolution In Two-Dimensional Integrable and Chaotic CFTs

We investigate the complex time evolution of a vacuum state with the insertion of a local primary operator in two-dimensional conformal field theories (2d CFTs). This complex time evolution can be considered as a composite process constructed from Lorentzian time evolution and a Euclidean evolution induced by a post-selected measurement. Our main finding is that in the spatially-compact system, this complex time evolution drives the state of the subsystems to those of the primary state with the same conformal dimensions of the inserted operator. Contrary to the compact system, the subsystems of the spatially non-compact system evolve to states that depend on the non-unitary process during a certain time regime. In holographic systems with a compact spatial direction, this process induced by a heavy local operator can correspond to the relaxation from a black hole with an inhomogeneous horizon to that with a uniform one, while in the ones with a non-compact spatial direction, it can correspond to the relaxation to that with a horizon depending on the non-unitary process.

hep-th↗

arXiv2025

Universal and Maximal Entanglement Swapping in General Fermionic Gaussian States

Exploring universal entanglement structure in many-body systems is both fundamental and challenging, particularly when the system undergoes non-unitary operations. In this work, we uncover a universal mechanism for realizing maximal entanglement swapping in fermionic Gaussian states subjected to projective Bell measurements. We consider two initially decoupled, half-filled copies of a free-fermion system in arbitrary dimensions and perform post-selective Bell measurements on half of the corresponding sites across the two copies. Remarkably, the post-measurement state factorizes into a product of Bell pairs, establishing maximal interlayer entanglement entirely independent of the initial Gaussian state. We derive this post-measurement state exactly for general particle-number-conserving fermionic Gaussian states, establishing both the validity and universality of the mechanism, with numerical simulations serving as consistency checks. This phenomenon arises from a robust interplay between fermionic statistics and Gaussianity, revealing a distinct fermionic route to measurement-induced maximal entanglement.

quant-ph↗

arXiv2025

Space of conformal boundary conditions from the view of higher Berry phase: Flow of Berry curvature in parametrized BCFTs

In this work, we study the connection between two subjects: the space of conformal boundary conditions in boundary conformal field theories (BCFTs) and the space of gapped systems characterized by higher Berry phases. We explore this connection by analyzing multi-parameter spectral flow in Dirac fermion BCFTs with continuously parametrized conformal boundary conditions, which are introduced by coupling a CFT to a family of gapped systems. When the gapped systems belong to a nontrivial higher Berry class, the associated conformal boundary conditions induce a flow of the ordinary Berry curvature, resulting in a Chern number pump in the Fock space of the BCFT. This phenomenon is the BCFT analog of Berry curvature flow in one-dimensional parametrized gapped systems, where the flow occurs in real space. Building on this correspondence, we introduce the notions of higher Berry curvature and higher Berry invariants within the BCFT framework. Our results provide a new perspective for studying the topological properties of families of conformal boundary states and gapped ground states: if a family of gapped states belongs to a nontrivial higher Berry class, then the corresponding entanglement Hamiltonians exhibit a multi-parameter spectral flow that carries Berry curvature in the Fock space.

hep-th↗

arXiv2025

Impurity-induced non-unitary criticality

Quantum impurities give rise to rich physical phenomena, with some exhibiting critical behavior described by conformal field theories (CFTs) in the low-energy limit. In parallel, party-time ($\mathcal{PT}$) symmetric non-Hermitian systems host exceptional points (EPs) at criticality, leading to exotic features governed by non-unitary CFTs. Here, we establish a connection between non-Hermitian impurities and CFTs by demonstrating that the critical properties of a (1+1)-dimensional free-fermion chain with central charge $c=1$ can be drastically altered by the presence of a local non-Hermitian impurity. Through a systematic analysis of entanglement/Rényi entropy, the finite-size scaling of the many-body spectrum, and fidelity susceptibility, we identify that this impurity-induced non-Hermitian criticality is characterized by a non-unitary CFT with central charge $c=-2$. Furthermore, we find that these non-unitary critical properties exhibit strong sensitivity to boundary conditions.

quant-ph↗

arXiv2025

Charting the space of ground states with tensor networks

We employ matrix product states (MPS) and tensor networks to study topological properties of the space of ground states of gapped many-body systems. We focus on families of states in one spatial dimension, where each state can be represented as an injective MPS of finite bond dimension. Such states are short-range entangled ground states of gapped local Hamiltonians. To such parametrized families over $X$ we associate a gerbe, which generalizes the line bundle of ground states in zero-dimensional families (\emph{i.e.} in few-body quantum mechanics). The nontriviality of the gerbe is measured by a class in $H^3(X, \mathbb{Z})$, which is believed to classify one-dimensional parametrized systems. We show that when the gerbe is nontrivial, there is an obstruction to representing the family of ground states with an MPS tensor that is continuous everywhere on $X$. We illustrate our construction with two examples of nontrivial parametrized systems over $X=S^3$ and $X = \mathbb{R} P^2 \times S^1$. Finally, we sketch using tensor network methods how the construction extends to higher dimensional parametrized systems, with an example of a two-dimensional parametrized system that gives rise to a nontrivial 2-gerbe over $X = S^4$.

cond-mat.str-el↗

arXiv2025

Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results

In this work, we study analytically the phase transitions in quasi-periodically driven one dimensional quantum critical systems that are described by conformal field theories (CFTs). The phase diagrams and phase transitions can be analytically obtained by using Avila's global theory in one-frequency quasiperiodic cocycles. Compared to the previous works where the quasiperiodicity was introduced in the driving time and no phase transitions were observed [1], here we propose a setup where the quasiperiodicity is introduced in the driving Hamiltonians. In our setup, one can observe the heating phases, non-heating phases, and the phase transitions. The phase diagram as well as the Lyapunov exponents that determine the entanglement entropy evolution can be analytically obtained. In addition, based on Avila's theory, we prove there is no phase transition in the previously proposed setup of quasi-periodically driven CFTs [1]. We verify our field theory results by studying the time evolution of entanglement entropy on lattice models.

cond-mat.stat-mech↗

arXiv2024

Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking

The global symmetry, either invertible or non-invertible, has been extensively studied in two dimensional conformal field theories in recent years. When the theory is defined on a manifold with open boundaries, however, many interesting conformal boundary conditions will fully or partially break such global symmetry. In this work, we study the effect of symmetry-breaking boundaries or interfaces when the system is out of equilibrium. We show that the boundary or interface symmetry-breaking can be detected by the time evolution of string order parameters, which are constructed from the symmetry operators that implement the symmetry transformations. While the string order parameters are independent of time if the symmetry is preserved over the whole system, they evolve in time in a universal way if the boundary or interface breaks the symmetry. More explicitly, in the presence of boundary or interface symmetry-breaking, the string order parameters decay exponentially in time after a global quantum quench, and decay as a power-law in time after a local quantum quench. We also generalize our study to the case when the string order parameters are defined in a subsystem, which are related to the full counting statistics. It is found there are also universal features in the time evolution of string order parameters in this case. We verify our field theory results by studying the time evolution of these two different types of string order parameters in lattice models.

cond-mat.str-el↗

arXiv2024

A critical state under weak measurement is not critical

Critical systems host nontrivial entanglement structure that is generally sensitive to additional couplings. In the present work, we study the effect of weak measurements on the entanglement Hamiltonian of massless free fermions which are prepared in their critical ground state. While the power-law decaying correlation and logarithmic growing entanglement entropy have been observed as typical signatures of quantum criticality after the weak measurement, in this work we show that the conformal symmetry is lost and the entanglement Hamiltonian generally becomes gapped for arbitrary small measurement strength. To reveal this unconventional entanglement structure, we consider a field-theory description that allows us to establish an analytic mapping between the entanglement Hamiltonians before and after the weak measurements. From this mapping, we find that although the measurements lead to a significant modification of the entanglement spectrum, the real-space distribution of the eigenfunction of the kernel of entanglement Hamiltonian is unchanged, which is responsible for the coexistence of a gapped entanglement Hamiltonian and the logarithmic entanglement entropy. Moreover, as the mapping works for arbitrarily many disjoint intervals, the multi-interval entanglement entropy also exhibits the same scaling behavior as the critical ground state, and shares the same effective central charge with the single-interval case. We numerically demonstrate these field-theory results on a lattice model, where the entanglement Hamiltonian after weak measurements exhibits the typical signature of a finite gap and becomes long-ranged even in the single-interval case. This is distinct from the critical ground state, where the entanglement Hamiltonian for a single interval is gapless and local.

cond-mat.stat-mech↗

arXiv2024

Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics

In this series of works, we study exactly solvable non-unitary time evolutions in one-dimensional quantum critical systems ranging from quantum quenches to time-dependent drivings. In this part I, we are motivated by the recent works of Kontsevich and Segal [1] and Witten [2] on allowable complex spacetime metrics in quantum field theories. In general, such complex spacetime metrics will lead to non-unitary time evolutions. In this work, we study the universal features of such non-unitary time evolutions based on exactly solvable setups. Various physical quantities including entanglement Hamiltonian and entanglement spectrum, entanglement entropy, and energy density at an arbitrary time can be exactly solved. Due to the damping effect introduced by the complex time, the excitations in the initial state are gradually damped out in time. The non-equilibrium dynamics exhibits universal features that are qualitatively different from the case of real-time evolutions. For instance, for an infinite system after a global quench, the entanglement entropy of the semi-infinite subsystem will grow logarithmically in time, in contrast to the linear growth in a real-time evolution. Moreover, we study numerically the time-dependent driven quantum critical systems with allowable complex spacetime metrics. It is found that the competition between driving and damping leads to a steady state with an interesting entanglement structure.

cond-mat.stat-mech↗

arXiv2024

Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension

We propose a systematic wave function based approach to construct topological invariants for families of lattice systems that are short-range entangled using local parameter spaces. This construction is particularly suitable when given a family of tensor networks that can be viewed as the ground states of $d$ dimensional lattice systems, for which we construct the closed $(d+2)$-form higher Berry curvature, which is a generalization of the well known 2-form Berry curvature. Such $(d+2)$-form higher Berry curvature characterizes a flow of $(d+1)$-form higher Berry curvature in the system. Our construction is equally suitable for constructing other higher pumps, such as the (higher) Thouless pump in the presence of a global on-site $U(1)$ symmetry, which corresponds to a closed $d$-form. The cohomology classes of such higher differential forms are topological invariants and are expected to be quantized for short-range entangled states. We illustrate our construction with exactly solvable lattice models that are in nontrivial higher Berry classes in $d=2$.

cond-mat.str-el↗

arXiv2024

Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States

Higher Berry curvature (HBC) is the proposed generalization of Berry curvature to infinitely extended systems. Heuristically HBC captures the flow of local Berry curvature in a system. Here we provide a simple formula for computing the HBC for extended $d = 1$ systems at the level of wave functions using the Schmidt decomposition. We also find a corresponding formula for matrix product states (MPS), and show that for translationally invariant MPS this gives rise to a quantized invariant. We demonstrate our approach with an exactly solvable model and numerical calculations for generic models using iDMRG

cond-mat.str-el↗

arXiv2024

Universal entanglement signatures of interface conformal field theories

An interface connecting two distinct conformal field theories hosts rich critical behaviors. In this work, we investigate the entanglement properties of such critical interface theories for probing the underlying universality. As inspired by holographic perspectives, we demonstrate vital features of various entanglement measures regarding such interfaces based on several paradigmatic lattice models. Crucially, for two subsystems adjacent at the interface, the mutual information and the reflected entropy exhibit identical leading logarithmic scaling, giving an effective interface central charge that takes the same value as the smaller central charge of the two conformal field theories. Our work demonstrates that the entanglement measure offers a powerful tool to explore the rich physics in critical interface theories.

cond-mat.stat-mech↗

arXiv2022

Floquet's Refrigerator: Conformal Cooling in Driven Quantum Critical Systems

We propose a general method of cooling -- periodic driving generated by spatially deformed Hamiltonians -- and study it in general one-dimensional quantum critical systems described by a conformal field theory. Our protocol is able to efficiently cool a finite-temperature Gibbs (mixed) state down to zero temperature at prescribed sub-regions exponentially rapidly in Floquet time cycles. At the same time, entropy and energy are transferred and localized to the complementary regions that shrink with time. We derive these conclusions through an exact analytic solution of the full time evolution of reduced density matrices. We also use numerics in free-fermion lattice models as a benchmark and find remarkable agreement. Such conformal Floquet refrigerators open a promising new route to cooling synthetic quantum systems.

cond-mat.str-el↗

arXiv2022

Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases

In this sequel (to [Phys. Rev. Res. 3, 023044(2021)], arXiv:2006.10072), we study randomly driven $(1+1)$ dimensional conformal field theories (CFTs), a family of quantum many-body systems with soluble non-equilibrium quantum dynamics. The sequence of driving Hamiltonians is drawn from an independent and identically distributed random ensemble. At each driving step, the deformed Hamiltonian only involves the energy-momentum density spatially modulated at a single wavelength and therefore induces a Möbius transformation on the complex coordinates. The non-equilibrium dynamics is then determined by the corresponding sequence of Möbius transformations, from which the Lyapunov exponent $λ_L$ is defined. We use Furstenberg's theorem to classify the dynamical phases and show that except for a few \emph{exceptional points} that do not satisfy Furstenberg's criteria, the random drivings always lead to a heating phase with the total energy growing exponentially in the number of driving steps $n$ and the subsystem entanglement entropy growing linearly in $n$ with a slope proportional to central charge $c$ and the Lyapunov exponent $λ_L$. On the contrary, the subsystem entanglement entropy at an exceptional point could grow as $\sqrt{n}$ while the total energy remains to grow exponentially. In addition, we show that the distributions of the operator evolution and the energy density peaks are also useful characterizations to distinguish the heating phase from the exceptional points: the heating phase has both distributions to be continuous, while the exceptional points could support finite convex combinations of Dirac measures depending on their specific type. In the end, we compare the field theory results with the lattice model calculations for both the entanglement and energy evolution and find remarkably good agreement.

cond-mat.stat-mech↗