Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this article, we describe how a loop series expansion can be applied to systematically improve the accuracy of a BP approximation to a tensor network contraction, in principle converging arbitrarily close to the exact result. More generally, our result provides a framework for expanding a tensor network as a sum of component networks in a hierarchy of increasing complexity. We benchmark this proposal for the contraction of infinite projected entangled pair states, either representing the ground state of an Affleck-Kennedy-Lieb-Tasaki (AKLT) model or with randomly defined tensors, where it is shown to improve in accuracy over standard BP by several orders of magnitude while incurring only a minor increase in computational cost. These results indicate that the proposed series expansions could be a useful tool to accurately evaluate tensor networks in cases that otherwise exceed the limits of established contraction routines.

Magnetic domain walls (DWs) are topological defects that host robust low-energy modes, which can be harnessed for classical and neuromorphic computing. However, accessing their quantum dynamics has remained an outstanding challenge. Using concepts from cavity optomechanics, we show that a geometric, Coriolis-type interaction between localized DWs and extended magnon modes in short insulating ferromagnetic wires enables efficient cooling of DWs to their quantum ground state and the preparation of nonclassical states with negative Wigner functions, detectable in the power spectrum of emitted magnons. We further demonstrate that magnons can mediate long-range entangling interactions between qubits encoded in spatially separated DWs, providing a route toward universal quantum gate operations. Our proposal relies solely on intrinsic degrees of freedom of the ferromagnet and naturally extends to ferrimagnets and antiferromagnets, as well as to other confined magnetic textures such as vortices and skyrmions in insulating nanostructures.

Stability and efficiency are mutually exclusive in a thermodynamic process, e.g., in a thermal machine. Any effort to reduce the fluctuations of a certain output quantity is necessarily accompanied by an increase of entropy production, therefore lowering its efficiency. This interplay is beautifully captured by the so-called thermodynamic uncertainty relations (TURs), which set a lower bound on the relative uncertainty of a current for a given rate of entropy production. Their status in hybrid normal-superconducting (N-S) devices has remained unsettled. We show that, in the subgap regime, departures from the normal quantum TUR are governed by macroscopic superconducting coherence quantified by the pair amplitude, and that introducing a dephasing probe suppresses this coherence and restores the bound. We further derive a hybrid quantum TUR that is general for two-terminal N-S junctions in the Andreev regime: the inequality is never violated, is saturated only at vanishing current, and is related to the normal quantum bound under the replacement $e\to 2e$. For N-S quantum dot and Cooper-pair-splitter systems, we compute current and noise and show that deviations from the normal bound track the pair amplitude on the central region. The results establish a direct link between superconducting macroscopic coherence and nonequilibrium fluctuations and supply a general bound for the Andreev regime.

We present an experimental and theoretical study of the infrared-active phonon modes of heavily potassium (K) doped $p$-terphenyl, a material of great current interest due to reports of high-temperature superconductivity. First, we show that the phonon features in the fingerprint region of the midinfrared domain can be well reproduced through the density functional theory (DFT) quantum-chemical simulations. Compelling evidence for a distorted organic molecular framework is obtained here from the emergence of up to three absorption bands that are predicted to be infrared (IR)-inactive under idealized $D_{2h}$ planar symmetry and a systematic softening of specific vibrational modes. Computational models of twisted conformers exhibiting reduced $D_2$ or $C_{2h}$ symmetry are shown to successfully reproduce the activation of these silent modes and the redshifting shown by others. Second, we present an analysis of the lineshape of the experimental IR-phonon modes in a wide temperature range from 6 to 300 K. We show that several of the IR phonons have a strongly asymmetric shape that is indicative of a Fano-like interaction with the doped charge carriers. Notably, we find that the phonon asymmetries, and the corresponding Fano parameters, undergo anomalous changes around 100 K that are reminiscent of a charge localization transition around 90 K that has been previously reported from a corresponding study of the low-energy electronic response.

We present a broadband (THz to UV) ellipsometry study of the anisotropic dielectric response of the orthorhombic perovskite ${\mathrm{YAlO}}_3$. The ellipsometric measurements have been performed on ${\mathrm{YAlO}}_3$ crystals with three different surface cuts and for six high-symmetry configurations of the crystal axes with respect to the plane of incidence of the photons. The obtained data are presented in terms of the Mueller matrix elements $N, C$, and $S$, and their features are analyzed and discussed with respect to the anisotropy of the dielectric response tensor. In particular, in the infrared range we have identified all 25 infrared-active phonon modes that have been predicted from theoretical studies. We also discuss a negative refraction effect that naturally occurs in the vicinity of an anisotropic longitudinal-optical phonon. Moreover, we have determined the temperature dependence of the phonon parameters between 10 and 330 K. The dielectric response above the phonon range, from about 0.1 to 6.5 eV, is shown to be featureless and characteristic of an insulator with a large band gap above 6.5 eV and is well described by anisotropic Cauchy model.

We classify gapped phases and characteristic nodal points of non-Hermitian band structures on two-dimensional nonorientable parameter spaces. Such spaces arise in a wide range of physical systems in the presence of nonsymmorphic parameter space symmetries. For gapped phases, we find that nonorientable spaces provide a natural setting for exploring fundamental structural problems in braid group theory, such as torsion and conjugacy. Gapless systems, which host exceptional points (EPs), explicitly violate fermion doubling, even in two-band models. We demonstrate that EPs traversing the nonorientable parameter space exhibit non-Abelian charge inversion. These braided phases and their transitions leave distinct signatures in the form of bulk Fermi arc degeneracies, offering a concrete route toward experimental realization and verification.

Complex fluids such as colloids and emulsions are ubiquitous in biopharmaceuticals, manufacturing, and the oil industry, but controlling their viscosity can pose a significant challenge. Low viscosities are ideal for mixing, high viscosities are helpful for pharmaceuticals, and switchable viscosities are useful for smart materials. One strategy to make multipurpose fluids is to make nonequilibrium modifications to the microstructure of colloids and emulsions using external fields, which can result in emergent changes in their rheological characteristics. We introduce an experimental technique, electrorheoimaging (ERI), which directly visualizes microstructure during rheological measurements while simultaneously applying an electric field. We also introduce a continuous phase that lowers electrohydrodynamic thresholds and enables experiments at modest field strengths, revealing behaviors previously inaccessible in laboratory settings. Using this combination of technique and material design, we observe shear-induced banding that only appears in the presence of electric depending on the frequency of the electric field, at either high or low shear rates. These microstructural transitions produce dramatic, reversible viscosity modulation—not only increases, but also decreases, including negative intrinsic viscosities. Frequency control enables instantaneous switching among multiple effective viscosities spanning a 30-fold range, establishing ERI as a powerful tool for probing and controlling rheology in field-responsive soft materials.

The elastic response of mechanical, chemical, and biological systems is often modeled using a discrete arrangement of Hookean springs, representing either finite material elements or even the molecular bonds of a system. However, to date, there is no direct derivation of the relation between a general discrete spring network, with arbitrary geometry, and its corresponding elastic continuum. Furthermore, understanding the network’s mechanical response requires simulations that may be expensive computationally. Here, we report a method to derive the exact elastic continuum model of any discrete network of springs, requiring network geometry and topology only. We identify and calculate the so-called “nonaffine” displacements. Explicit comparison of our calculations to simulations of different crystalline and disordered configurations shows that we successfully capture the mechanics even of auxetic materials. Our method is valid for residually stressed systems with nontrivial geometries, and is an important step in generalizing active stresses on such discrete systems. It is easily generalizable to other discrete models, and opens the possibility of a rational design of elastic systems.

Mode switching in exciton-polariton condensates represents a significant phenomenon that illustrates the non-Hermitian properties and out-of-equilibrium dynamics of exciton-polaritons. In this research, we experimentally demonstrate controllable mode switching in a tunable ZnO microrod cavity at room temperature, where increasing pump power drives the condensate from one lower polariton branch to another of higher energy. This unconventional up-switching is explained by an imbalance in the densities of the active excitonic reservoirs, governed by both loss and relaxation efficiency. Ultrafast spectroscopy reveals a several-picosecond delay between the condensates, providing direct evidence for this mechanism. Our results provide important insights into the fundamental physics of Bose-Einstein condensation in dissipative systems, enable control of polariton condensation through reservoir engineering, and open routes to room-temperature polaritonic devices exploiting nonlinear switching.

When focusing on a few essential bands in an effective description of a material to calculate observable quantities, the respective operators have to be adjusted accordingly. Ignoring contributions arising from integrating out remote bands can lead to qualitatively wrong results. We present a detailed analysis of the interband mixing effects on spin currents. Specifically, we calculate the intrinsic spin current in a time-reversal invariant noncentrosymmetric crystal in the presence of electron-lattice spin-orbit coupling. Starting from formally exact microscopic expressions, we derive the spin-current operator restricted to one or more essential bands by iterative elimination of the contributions from distant bands. We show that the standard definition of the spin-current operator in terms of the group velocity obtained from an effective band Hamiltonian cannot be justified using a microscopic theory. The modified expression for the spin-current operator contains additional terms, which dominate the equilibrium spin current in a uniform crystal. We show that the magnitude of these additional terms can considerably exceed the spin current obtained using the standard definition.

The magnetic Weyl semimetal ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ has garnered significant experimental and theoretical interest, particularly regarding its electronic structure and transport properties. In this study, we comprehensively investigated the effects of Fe and Ni substitution in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. The temperature-dependent Seebeck coefficient ($S$) implies that the reduction of the band gap and the shift in the Fermi level ($E_{\mathrm{F}}$) due to Fe and Ni substitution, which was supported by angle-resolved photoemission spectroscopy results. These band-structure modifications influence not only thermoelectric (TE) performance but also the anomalous Hall conductivity (${\sigma }_{\mathrm{xy}}^{\mathrm{A}}$). Specifically, Fe substitution increases ${\sigma }_{\mathrm{xy}}^{\mathrm{A}}$ via skew scattering, while Ni substitution increases ${\sigma }_{\mathrm{xy}}^{\mathrm{A}}$ via intrinsic deflection with minor skew scattering. Additionally, the Fe and Ni dopant-induced changes in the $c/a$ ratio were demonstrated using high-resolution powder synchrotron x-ray diffraction, which explains the different modulation in the magnetic anisotropy of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ due to the magnetostriction effect. Notably, the oxidation states of Co, Fe, and Ni in each single crystal were confirmed as 0 using x-ray absorption near-edge structure analysis, further explaining the dopant-induced suppression in ferromagnetism of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. These findings provide deeper insight into the band-filling effects on both TE and anomalous Hall transport in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$, offering perspectives for topological spintronics and TE applications.

Understanding quantum phases of matter is a fundamental goal in physics. For pure states, the representatives of phases are the ground states of locally interacting Hamiltonians, which are also renormalization fixed points (RFPs). These RFP states are exactly described by tensor networks. Extending this framework to mixed states, matrix product density operators (MPDOs) that are RFPs are believed to encapsulate mixed-state phases of matter in one dimension, where nontrivial topological phases have already been shown to exist. However, to better motivate the physical relevance of those states, and in particular the physical relevance of the recently found non trivial phases, it remains an open question whether such MPDO RFPs can be realized as steady states of local Lindbladians. In this work, we resolve this question by analytically constructing parent Lindbladians for MPDO RFPs. These Lindbladians are local, frustration free, and exhibit minimal steady-state degeneracy. Interestingly, we find that parent Lindbladians possess a rich structure that distinguishes them from their Hamiltonian counterparts. In particular, we uncover an intriguing connection between the noncommutativity of the Lindbladian terms and the fact that the corresponding MPDO RFP belongs to a nontrivial phase.

The quantum approximate optimization algorithm (QAOA) is a variational ansatz that resembles the Trotterized dynamics of a quantum annealing (QA) protocol. This work formalizes this connection formally and empirically, showing that the angles of a multilayer QAOA circuit converge to universal QA trajectories. Furthermore, the errors in both QAOA circuits and QA paths act as thermal excitations in pseudo-Boltzmann probability distributions whose temperature decreases with the invested resource—i.e., integrated angles or total time—and which in QAOA also contain a higher temperature arising from the Trotterization. This also means that QAOA and QA are cooling protocols and simulators of partition functions whose target temperature can be tuned by rescaling the universal trajectory. The average cooling power of both methods exhibits favorable algebraic scalings with respect to the target temperature and problem size, whereby in QAOA the coldest temperature is inversely proportional to the number of layers, $T\sim 1/p$, and to the integrated angles—or integrated interactions in QA.

Geometrical frustration in quantum magnets provides a fertile setting for unconventional phases of matter, including quantum spin liquids (QSLs). The trellis lattice, with its complex site arrangements and edge-sharing triangular motifs, presents a promising platform for such physics. In this work, we undertake a comprehensive classification of all fully symmetric QSLs on the trellis lattice using the projective symmetry group approach within the Abrikosov-fermion representation. We find 7 U(1) and 25 ${\mathbb{Z}}_2$ short-ranged Ansätze and analyze the phase diagram in the mean-field parameter space, uncovering both gapped and Dirac QSLs as well as a semi-Dirac spin liquid that emerges at the level of projective symmetry group classification and mean-field band structure, in which the spinon dispersion is linear along one momentum direction but quadratic along the orthogonal one. We demonstrate that such dispersions can occur only at high-symmetry points in the Brillouin zone with $C_{2v}$ little groups and analyze their characteristic correlation signatures. Moreover, by optimizing over all symmetry-allowed mean-field states, we map out a phase diagram—featuring six distinct phases—of the nearest-neighbor Heisenberg Hamiltonian on the trellis lattice. Among these, we find four quasi-one-dimensional QSL phases, one dimer phase, and one Dirac QSL phase. Going beyond mean field, we also assess equal-time and dynamical spin structure factors of these phases using density-matrix renormalization group and Keldysh pseudofermion functional renormalization group calculations and compare qualitative momentum-space features of these spectra with those obtained at the mean-field level. Finally, we identify four cuprate and vanadate compounds as promising experimental realizations and provide spectroscopic predictions, based on first-principles Hamiltonians, as a guide for future neutron-scattering studies on these materials.

Recent theoretical works predict a hierarchy of long-lived, nonhydrodynamic modes in two-dimensional Fermi liquids arising from the feature—supposedly unique to two dimensions—that relaxation by head-on scattering is not efficient in the presence of Pauli blocking. This leads to a parity-based separation of scattering rates, with odd-parity modes relaxing much more slowly than even-parity ones. In this work, we establish that a similar effect exists in isotropic three-dimensional (3D) Fermi liquids, even though relaxation does not proceed solely by head-on scattering. We show that while the relaxation rates of even and odd modes in 3D share the same leading-order $\sim T^2$ low-temperature scaling typical of Fermi liquids, their magnitudes differ, with odd-parity modes relaxing more slowly than even ones for a broad class of interactions. We find a relative difference between odd-parity and even-parity relaxation rates as large as $40\%$ just by Pauli blocking alone, with a strong additional dependence on the scattering potential, such that the odd-even staggering is further enhanced by interactions that favor large-angle scattering. We identify signatures of these odd-parity relaxation rates in the static transverse conductivity as well as the transverse collective mode structure. Our results establish the unexpected existence of a tomographiclike regime in higher-dimensional Fermi liquids and suggest experimental probes via transport measurements.

Semiconductor nanowires (NWs) with strong Rashba spin-orbit coupling (RSOC), when exposed to a suitably applied Zeeman field, exhibit one-dimensional helical channels with a spin orientation locked to the propagation direction within the magnetic energy gap. Here, by adopting a scattering-matrix approach applied to a tight-binding model of the NW, we demonstrate that the thermoelectric (TE) properties can be widely controlled by tuning the misalignment angle $\varphi$ between the spin-orbit directions of two NW segments. In particular, when the RSOC vectors are antiparallel (Dirac-paradox configuration), we predict a significant violation of the Wiedemann-Franz law, and a strong enhancement of the Seebeck coefficient and the $ZT$ figure of merit. We also show that the Zeeman gap determines the optimal energy window for doping and temperatures. These results suggest that controlling the spin-orbit field direction, which can be achieved with suitably applied wrap gates, is a promising alternative for tuning and optimizing the TE response in quantum-coherent semiconducting NW devices.

Skutterudites are promising materials for thermoelectric and spintronics applications. Here, we explore spin fluctuations in the ${\mathrm{FeSb}}_3$ skutterudite and their effect on its electronic structure using Hubbard-corrected density-functional theory calculations. We identify multiple magnetic- and charge-disproportionated configurations, with an antiferromagnetic metallic ground state. Paramagnetic fluctuations modeled through a special quasirandom spin structure open a 61 meV gap, consistent with experiments. This state features nondegenerate spin channels and band-avoided crossings, resembling a Luttinger-compensated ferrimagnet. Mapping the electronic structure to a Heisenberg Hamiltonian fails to explain the low Néel temperature ($\lesssim 10\mathrm{K}$), suggesting that factors such as stoichiometry and magnetic exchange frustration may play an important role, calling for more detailed experimental investigations.