The four-dimensional Chern-Simons (CS) theory provides a systematic procedure for realizing two-dimensional integrable field theories. It is therefore a natural question to ask whether integrable deformations of the theories can be realized in the four-dimensional CS theory. In this work, we study $T\bar{T}$ and root-$T\bar{T}$ deformations of two-dimensional integrable field theories, formulated in terms of dynamical coordinate transformations, within the framework of four-dimensional CS theory coupled to disorder defects. We illustrate our procedure in detail for the degenerate $\mathcal{E}$-model, a specific construction that captures and unifies a broad range of integrable systems, including the principal chiral model.

We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment for the entire system. Based on this optimized environment, we construct renormalization projectors that significantly enhance accuracy. By leveraging the canonical form of tensors, our algorithm maintains the same computational complexity as the original tensor renormalization group (TRG) method, yet achieves higher accuracy than existing approaches that do not incorporate entanglement filtering. Our work offers a practical pathway for extending TRG methods to higher dimensions while keeping computational costs manageable.

Quantum many-body scars (QMBS) serve as important examples of ergodicity-breaking phenomena in quantum many-body systems. Despite recent extensive studies, exact QMBS are rare in dimensions higher than one. In this paper, we study a two-dimensional quantum $\mathbb{Z}_2$ gauge model that is dual to a two-dimensional spin-$1/2$ XY model defined on bipartite graphs. We identify the exact eigenstates of the XY model with a tower structure as exact QMBS. Exploiting the duality transformation, we show that the exact QMBS of the XY model (and XXZ model) after the transformation are the exact QMBS of the dual $\mathbb{Z}_2$ gauge model. This construction is versatile and has potential applications for finding new QMBS in other higher-dimensional models.

Tellurium (Te), a two-dimensional material with pronounced structural anisotropy, exhibits exceptional electrical and optical properties that are highly sensitive to its crystallographic orientation. However, conventional synthesis techniques offer limited control over the in-plane alignment of Te's crystallographic c-axis, hindering large-scale integration. Here, we report a novel, non-contact method to dynamically manipulate the c-axis orientation of Te thin films using linearly polarized picosecond laser pulses. We show that the c-axis can be omnidirectionally reoriented perpendicular to the laser polarization, even in initially polycrystalline films. This reorientation is fully reversible, allowing for rewritable and spatially selective control of the c-axis orientation post-deposition. Our light-driven approach enables programmable anisotropy in Te, opening new avenues for reconfigurable optoelectronic and photonic devices, such as active metasurfaces and CMOS-compatible architectures.

Through coarse-graining, tensor network representations of a two-dimensional critical lattice model flow to a universal four-leg tensor, corresponding to a conformal field theory (CFT) fixed-point. We computed explicit elements of the critical fixed-point tensor, which we identify as the CFT four-point function. This allows us to directly extract the operator product expansion coefficients of the CFT from these tensor elements. Combined with the scaling dimensions obtained from the transfer matrix, we determine the complete set of the CFT data from the fixed-point tensor for any critical unitary lattice model.

Collective modes in superconductors, such as the Higgs mode, offer deep insights into the nature of condensates. Third-harmonic generation (THG) is a primary tool for probing the Higgs mode, but its signal competes with that of quasiparticle excitations depending on impurity scattering rates. In particular, in the clean regime the standard BCS theory generally predicts the dominance of quasiparticle contributions. Here, we propose and demonstrate that the quantum geometry of electronic bands can be a key mechanism governing this competition. By developing a formalism that explicitly incorporates the quantum metric, and applying it to a tunable model of a dispersive-band superconductor, we show that the quantum metric can dramatically amplify the nonlinear light-Higgs coupling by several orders of magnitude. Our results establish that a large quantum metric can cause the Higgs mode to dominate the THG response, resolving the puzzle of Higgs and quasiparticle competition in the clean regime and identifying band geometry as a crucial ingredient for designing and understanding the nonlinear response of superconductors.

We explore non-invertible symmetries in two-dimensional lattice models with subsystem $\mathbb Z_2$ symmetry. We introduce a subsystem $\mathbb Z_2$-gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers-Wannier transformation. The corresponding duality operators and defects are constructed by gaugings on the whole or half of the Hilbert space. By gauging twice, we derive fusion rules of duality operators and defects, which enriches ordinary Ising fusion rules with subsystem features. Subsystem Kramers-Wannier duality defects are mobile in both spatial directions, unlike the defects of invertible subsystem symmetries. We finally comment on the anomaly of the subsystem Kramers-Wannier duality symmetry, and discuss its subtleties.

We study the Hall effect in isolated flat-band systems (i.e., a flat band is separated from other bands) for a weak magnetic field. In a naive semiclassical picture, the Hall conductivity vanishes when dispersive bands are unoccupied since there is no mobile carrier. To go beyond the semiclassical picture, we establish a fully quantum mechanical gauge-invariant formula for the Hall conductivity that can be applied to any lattice models. We apply the formula to a general two-band model with one dispersive and one isolated flat band, and find that the total conductivity takes a universal form as an integral of a product of the squared Berry curvature and energy difference between the two bands. In particular, the Hall coefficient can become nonzero in the flat-band systems with broken inversion symmetry. We numerically confirm this Hall effect for an isolated flat-band lattice model on the honeycomb lattice.

It has recently been suggested that at the post-inflationary stage of the mixed Higgs-$R^2$ model of inflation efficient particle production can arise from the tachyonic instability of the Higgs field. It might complete the preheating of the Universe if appropriate conditions are satisfied, especially in the Higgs-like regime. In this paper, we study this behavior in more depth, including the conditions for occurrence, analytical estimates for the maximal efficiency, and the necessary degree of fine-tuning among the model parameters to complete preheating by this effect. We find that the parameter sets that cause the most efficient tachyonic instabilities obey simple laws in both the Higgs-like regime and the $R^2$-like regime, respectively. We then estimate the efficiency of this instability. In particular, even in the deep $R^2$-like regime with a small non-minimal coupling, this effect is strong enough to complete preheating although a severe fine-tuning is required among the model parameters. We also estimate how much fine-tuning is needed to complete preheating by this effect. It is shown that the fine-tuning of parameters for the sufficient particle production is at least < \mathcal{O}(0.1) in the deep Higgs-like regime with a large scalaron mass, while it is more severe $\sim {\cal O}(10^{-4})-{\cal O}(10^{-5})$ in the $R^2$-like regime with a small non-minimal coupling.

The most widely studied formation mechanism of a primordial black hole is collapse of large-amplitude perturbation on small scales generated in single-field inflation. In this Letter, we calculate one-loop correction to the large-scale power spectrum in a model with sharp transition of the second slow-roll parameter. We find that models producing an appreciable amount of primordial black holes induce nonperturbative coupling on a large scale probed by cosmic microwave background radiation. Our result implies that a small-scale power spectrum can be constrained by large-scale cosmological observations.

We present the microscopic theory of the spin Nernst effect, which is a transverse spin current directly induced by a temperature gradient, employing the linear response theory with Luttinger's gravitational potential method. We consider a generic, non-interacting electron system with randomly distributed impurities and evaluate the spin current response to the gravitational potential. Our theory takes into account a contribution of the local equilibrium current modified by Luttinger's gravitational potential and is thus consistent with the thermodynamic principle that thermal responses should vanish. The Ward-Takahashi identities ensure that the spin Nernst current is well-behaved at low temperatures in any order of the random impurity potentials. Furthermore, we microscopically derive the spin-current version of Mott's formula, which associates the spin Nernst coefficient with the spin Hall conductivity. The spin-current version of the Středa formula is also discussed. To demonstrate these findings, the spin Nernst current of three-dimensional Dirac electrons is computed. Our theory is general and can therefore be extended to interacting electron systems, where Mott's formula no longer holds.

This work considers a teleportation task for Alice and Bob in a scenario where Bob cannot perform corrections. In particular, we analyse the task of \textit{multicopy state teleportation}, where Alice has $k$ identical copies of an arbitrary unknown $d$-dimensional qudit state $\vert\psi\rangle$ to teleport a single copy of $\vert\psi\rangle$ to Bob using a maximally entangled two-qudit state shared between Alice and Bob without Bob's correction. Alice may perform a joint measurement on her half of the entangled state and the $k$ copies of $\vert\psi\rangle$. We prove that the maximal probability of success for teleporting the exact state $\vert\psi\rangle$ to Bob is $p(d,k)=\frac{k}{d(k-1+d)}$ and present an explicit protocol to attain this performance. Then, by utilising $k$ copies of an arbitrary target state $\vert\psi\rangle$, we show how the multicopy state teleportation protocol can be employed to enhance the success probability of storage and retrieval of quantum programs, which aims to universally retrieve the action of an arbitrary quantum channel that is stored in a state. Our proofs make use of group representation theory methods, which may find applications beyond the problems addressed in this work.

We derive an exact residue formula for the elliptic genera of 2d $\mathcal{N}=(0,1)$ gauge theories. We find a new residue prescription which recovers the Jeffery-Kirwan residue prescription for $\mathcal{N}=(0,2)$ theories. We apply the formula to the Gukov-Pei-Putrov model and analyze the phase structure of the theory.

We analyze the quantum Hopfield model in which an extensive number of patterns are embedded in the presence of a uniform transverse field. This analysis employs the replica method under the replica symmetric ansatz on the Suzuki-Trotter representation of the model, while keeping the number of Trotter slices $M$ finite. The statistical properties of the quantum Hopfield model in imaginary time are reduced to an effective $M$-spin long-range classical Ising model, which can be extensively studied using a dedicated Monte Carlo algorithm. This approach contrasts with the commonly applied static approximation, which ignores the imaginary time dependency of the order parameters, but allows $M \to \infty$ to be taken analytically. During the analysis, we introduce an exact but fundamentally weaker static relation, referred to as the quasi-static relation. We present the phase diagram of the model with respect to the transverse field strength and the number of embedded patterns, indicating a small but quantitative difference from previous results obtained using the static approximation.

To understand the unexpectedly high thermoelectric performance observed in the thin-film Heusler alloy Fe$_2$V$_{0.8}$W$_{0.2}$Al, we study the magnon drag effect, generated by the tungsten based impurity band, as a possible source of this enhancement, in analogy to the phonon drag observed in FeSb$_2$. Assuming that the thin-film Heusler alloy has a conduction band integrating with the impurity band, originated by the tungsten substitution, we derive the electrical conductivity $L_{11}$ based on the self-consistent t-matrix approximation and the thermoelectric conductivity $L_{12}$ due to magnon drag, based on the linear response theory, and estimate the temperature dependent electrical resistivity, Seebeck coefficient and power factor. Finally, we compare the theoretical results with the experimental results of the thin-film Heusler alloy to show that the origin of the exceptional thermoelectric properties is likely to be due to the magnon drag related with the tungsten-based impurity band.

We give a characterization of a finite-dimensional commuting square of C*-algebras with a normalized trace that produces a hyperfinite type II_1 subfactor of finite index and finite depth in terms of Morita equivalent unitary fusion categories. This type of commuting squares were studied by N. Sato, and we show that a slight generalization of his construction covers the fully general case of such commuting squares. We also give a characterization of such a commuting square that produces a given hyperfinite type II_1 subfactor of finite index and finite depth. These results also give a characterization of certain 4-tensors that appear in recent studies of matrix product operators in 2-dimensional topological order.

Spin currents proportional to the first- and second-order of the electric field are calculated in a specific tight-binding model with time-reversal symmetry. Specifically, a tight-binding model with time-reversal symmetry is constructed with chiral hopping and spin-orbit coupling. The spin conductivity of the model is calculated using the Boltzmann equation. As a result, it is clarified that the first-order spin current of the electric field vanishes, while the second-order spin current can be finite. Furthermore, the spin current changes its sign by reversing the chirality of the model. The present results reveal the existence of spin currents in systems with time-reversal symmetry depending on the chirality of the system. They may provide useful information for understanding the chirality-dependent spin polarization phenomena in systems with time-reversal symmetry.

We study a class of newly-introduced CFTs associated with even quadratic forms of general signature, which we call generalized Narain theories. We first summarize the properties of these theories. We then consider orbifolds of these theories, thereby obtaining a large class of non-supersymmetric CFTs with exactly marginal deformations. We then discuss ensemble averages of such theories over their moduli space, and obtain a modular form associated with the quadratic form and an element of the discriminant group. The modular form can be written as a Poincare series, which contains novel invariants of lens spaces and suggests the interpretation of the holographic bulk as a theory of anyons.