We study the effects of disorder (quenched randomness) in a two-dimensional square-lattice $S=1/2$ quantum-spin system, the $J\text{−}Q$ model with a multispin interaction $Q$ supplementing the Heisenberg exchange $J$. In the absence of disorder, the system hosts antiferromagnetic (AFM) and columnar valence-bond-solid (VBS) ground states. The VBS breaks $Z_4$ symmetry spontaneously, and in the presence of arbitrarily weak disorder it forms domains. Using quantum Monte Carlo simulations, we demonstrate two different kinds of such disordered VBS states. Upon dilution, a removed site in one sublattice forces a leftover localized spin in the opposite sublattice. Such spins interact through the host system and always form AFM order. In the case of random-$J$ or -$Q$ interactions in the intact lattice, we find a different spin-liquid-like state with no magnetic or VBS order but with algebraically decaying mean correlations. Here we identify localized spinons at the nexus of domain walls separating regions with the four different VBS patterns. These spinons form correlated groups with the same number of spinons and antispinons. Within such a group, we argue that there is a strong tendency to singlet formation because of the native pairing and relatively strong spinon-spinon interactions mediated by the domain walls. Thus, the spinon groups are effectively isolated from each other and no long-range AFM order forms. The mean spin correlations decay as $r^{-2}$ as a function of distance $r$. We propose that this state is a two-dimensional analogue of the well-known random-singlet (RS) state in one dimension, though, in contrast to the one-dimensional case the dynamic exponent $z$ is finite in two dimensions. By studying quantum-critical scaling of the magnetic susceptibility, we find that $z$ varies, taking the value $z=2$ at the AFM-RS phase boundary and growing upon moving into the RS phase (thus, causing a power-law divergent susceptibility). The RS state discovered here in a system without geometric frustration may correspond to the same fixed point as the RS state recently proposed for frustrated systems, and the ability to study it without Monte Carlo sign problems opens up opportunities for further detailed characterization of its static and dynamic properties. We also discuss experimental evidence of the RS phase in the quasi-two-dimensional square-lattice random-exchange quantum magnets ${\mathrm{Sr}}_2{\mathrm{CuTe}}_{1-x}{\mathrm{W}}_x{\mathrm{O}}_6$ for $x$ in the range of 0.2–0.5.

In quantum materials with multiple degrees of freedom such as itinerant electrons and local moments, the interplay between them leads to intriguing phenomena and allows the mutual control of each other. Here, we study band topology and engineering from the interplay between local moments and itinerant electrons in pyrochlore iridates. For metallic ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, the Ir $5d$ conduction electrons interact with the Pr $4f$ local moments via the $f\text{−}d$ exchange. While the Ir electrons form a Luttinger semimetal, the Pr moments can be tuned into an ordered spin ice with a finite ordering wave vector, dubbed the Melko-Hertog-Gingras state, by varying Ir and O contents. We point out that the Pr Ising order generates an internal field and reconstructs the Ir bands. Besides the broad existence of Weyl nodes, we predict that the magnetic translation of the Pr Melko-Hertog-Gingras state protects the Dirac-band touching at certain time-reversal invariant momenta for the Ir electrons. We propose the magnetic fields to control the Pr magnetism and thereby indirectly influence the Ir conduction electrons. Our prediction can be immediately tested in ordered ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ samples. Our theory should stimulate experiments on pyrochlore iridates, constitute a nontrivial and realistic example for the interplay between itinerant electrons and local moments in three dimensions, and shed light on hybrid quantum materials with multiple degrees of freedom.

In sight of fundamental thermal limits on further substantial performance improvements of modern digital computational processing units, wave-based analog computation is becoming an enticing alternative. A wave, as it propagates through a carefully tailored medium, performs the desired computational operation. Yet, the necessary designs are so intricate that experimental demonstrations will necessitate further technological advances. Here, we show that, counterintuitively, the carefully tailored medium can be replaced with a random medium, subject to an appropriate shaping of the incident wave front. Using tunable metasurface reflect-arrays, we demonstrate our concept experimentally in a chaotic microwave cavity. We conclude that off-the-shelf wireless communication infrastructure in combination with a simple reflect-array suffices to perform analog computation with Wi-Fi waves reverberating in a room.

We study the barocaloric effect (BCE) in the geometrically frustrated antiferromagnet ${\mathrm{Mn}}_3\mathrm{NiN}$ across the Néel transition temperature. Experimentally, we find a larger barocaloric entropy change by a factor of 1.6 than that recently discovered in the isostructural antiperovskite ${\mathrm{Mn}}_3\mathrm{GaN}$ despite significantly greater magnetovolume coupling in ${\mathrm{Mn}}_3\mathrm{GaN}$. By fitting experimental data to theory, we show that the larger BCE of ${\mathrm{Mn}}_3\mathrm{NiN}$ originates from multisite exchange interactions amongst the local Mn magnetic moments and their coupling with itinerant electron spins. Using this framework, we discuss the route to maximize the BCE in the wider ${\mathrm{Mn}}_{3}A\mathrm{N}$ family.

We analyze the problem of extracting the correlation length from infinite matrix product states (MPS) and corner transfer matrix (CTM) simulations. When the correlation length is calculated directly from the transfer matrix, it is typically significantly underestimated for finite bond dimensions used in numerical simulation. This is true even when one considers ground states at a distance from the critical point. In this article we introduce extrapolation procedure to overcome this problem. To that end we quantify how much the dominant part of the MPS (as well as CTM) transfer matrix spectrum deviates from being continuous. The latter is necessary to capture the exact asymptotics of the correlation function where the exponential decay is typically modified by an additional algebraic term. By extrapolating such a refinement parameter to zero, we show that we are able to recover the exact value of the correlation length with high accuracy. In a generic setting, our method reduces the error by a factor of $\sim 100$ as compared to the results obtained without extrapolation and a factor of $\sim 10$ as compared to simple extrapolation schemes employing bond dimension. We test our approach in a number of solvable models both in 1D and 2D. Subsequently, we apply it to one-dimensional XXZ spin-$3/2$ and the Bose-Hubbard models in a massive regime in the vicinity of the Berezinskii-Kosterlitz-Thouless critical point. We then fit the scaling form of the correlation length and extract the position of the critical point and obtain results comparable or better than those of other state-of-the-art numerical methods. Finally, we show how the algebraic part of the correlation function asymptotics can be directly recovered from the scaling of the dominant form factor within our approach. Our method provides the means for detailed studies of phase diagrams of quantum models in 1D and, through the finite correlation length scaling of projected entangled pair states, also in 2D.

We study a 1D chain of noninteracting bosonic cavities which are subject to nearest-neighbor parametric driving, thus realizing a bosonic Hamiltonian whose form is reminiscent of the celebrated Kitaev model of a 1D $p$-wave superconductor. For a suitable choice of drive phases, the model exhibits a number of remarkable properties. This includes phase-dependent chirality: Photons propagate and are amplified in a direction determined by the phase of the initial drive or excitation. It also exhibits a drastic sensitivity to boundary conditions: For a range of parameters, the boundaryless system has only delocalized, dynamically unstable modes, while a finite open chain is described by localized, dynamically stable modes. While our model is described by a Hermitian Hamiltonian, we show that it has a surprising connection to non-Hermitian asymmetric hopping models. In addition to being of fundamental interest as a new kind of topological bosonic system, our system also has potential practical utility as a quantum amplifier and a source of multimode entangled photons.

Recent developments of experimental techniques have given us unprecedented opportunities of studying topological insulators in high dimensions, while some of the dimensions are “synthetic,” in the sense that the effective lattice momenta along these synthetic dimensions are controllable periodic tuning parameters. In this work, we study interaction effects on topological insulators with synthetic dimensions. We show that, although the free fermion band structure of high-dimensional topological insulators can be precisely simulated with the “synthetic techniques,” the generic interactions in these effective synthetic topological insulators are qualitatively different from the local interactions in ordinary condensed-matter systems. And we show that these special but generic interactions have unexpected effects on topological insulators; namely, they change (or reduce) the classification of topological insulators differently from the previously extensively studied local interactions.

In two-dimensional honeycomb ferromagnets, bosonic magnon quasiparticles (spin waves) may either behave as massless Dirac fermions or form topologically protected edge states. The key ingredient defining their nature is the next-nearest-neighbor Dzyaloshinskii-Moriya interaction that breaks the inversion symmetry of the lattice and discriminates chirality of the associated spin-wave excitations. Using inelastic neutron scattering, we find that spin waves of the insulating honeycomb ferromagnet ${\mathrm{CrI}}_3$ ($T_C=61\mathrm{K}$) have two distinctive bands of ferromagnetic excitations separated by a $\sim 4\mathrm{meV}$ gap at the Dirac points. These results can only be understood by considering a Heisenberg Hamiltonian with Dzyaloshinskii-Moriya interaction, thus providing experimental evidence that spin waves in ${\mathrm{CrI}}_3$ can have robust topological properties potentially useful for dissipationless spintronic applications.

We present a theory of the high-spin generalization of topological insulators and their doped superconducting states. The higher-spin topological insulators involve a pair of $J=3/2$ bands with opposite parity and are characterized by their band inversion. The low-energy effective theory reveals that the topological insulators host four different phases characterized by mirror Chern numbers, at which boundaries two different patterns of bulk Dirac points appear. For the carrier-doped case, it is shown that the system may host unique unconventional superconductivity because of its high-spin nature and additional orbital degrees of freedom intrinsic to topological insulators. The superconducting critical temperature is evaluated by using density-density pairing interactions, and odd-parity Cooper pairs are shown to be naturally realized in the presence of interorbital pairing interaction. It is observed that even the simplest spin-0 odd-parity pairing state exhibits a novel class of topological superconductivity—high winding topological superconductivity. We also discuss the experimental signals of high winding topological superconductivity in the case of the antiperovskite superconductor ${\mathrm{Sr}}_{3-x}\mathrm{SnO}$.

${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ hosts both topological surface states and bulk superconductivity. It has been identified recently as a topological superconductor (TSC) with an extraordinary nematic, i.e., $C_2$-symmetric superconducting state and odd-parity pairing. Here, using scanning tunneling microscopy, we directly examine the response of the superconductivity of ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ to magnetic field. Under out-of-plane fields ($B_{\perp }$), we discover elongated magnetic vortices hosting zero-bias conductance peaks consistent with the Majorana bound states expected in a TSC. Under in-plane fields ($B_{//}$), the average superconducting gap exhibits twofold symmetry with field orientation; the long $C_2$ symmetry axes are pinned to the dihedral mirror planes under $B_{//}=0.5\mathrm{T}$ but rotate slightly under $B_{//}=1.0\mathrm{T}$. Moreover, a nodeless ${\mathrm{\Delta }}_{4x}$ gap structure is semiquantitatively determined for the first time. Our data paint a microscopic picture of the nematic superconductivity in ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ and pose strong constraints on theory.

We focus on a broad class of tetragonal itinerant systems sharing a tendency towards the spontaneous formation of incommensurate magnetism with ordering wave vectors ${\mathit{Q}}_{1,2}=(\pi -\delta ,0)/(0,\pi -\delta )$ or ${\mathit{Q}}_{1,2}=(\pi ,\delta )/(-\delta ,\pi )$. Employing a Landau approach, we obtain the generic magnetic phase diagram and identify the leading instabilities near the paramagnetic-magnetic transition. Nine distinct magnetic phases exist that either preserve or violate the assumed $C_4$ symmetry of the paramagnetic phase. These are single- and double-$\mathit{Q}$ phases consisting of magnetic stripes, helices, and whirls, either in an individual or coexisting manner. These nine phases can be experimentally distinguished by polarized neutron scattering, or, e.g., by combining measurements of the induced charge order and magnetoelectric coupling. Within two representative five-orbital models, suitable for ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and LaFeAsO, we find that the incommensurate magnetic phases we discuss here are accessible in iron-based superconductors. Our investigation unveils a set of potential candidates for the unidentified $C_2$-symmetric magnetic phase that was recently observed in ${\mathrm{Ba}}_{1-x}{\mathrm{Na}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$. Among the phases stabilized we find a spin-whirl crystal, which is a textured magnetic $C_4$-symmetric phase. The possible experimental observation of textured magnetic orders in iron-based superconductors opens new directions for realizing intrinsic topological superconductors.

A thorough in situ characterization of materials at extreme conditions is challenging, and computational tools such as crystal structural search methods in combination with ab initio calculations are widely used to guide experiments by predicting the composition, structure, and properties of high-pressure compounds. However, such techniques are usually computationally expensive and not suitable for large-scale combinatorial exploration. On the other hand, data-driven computational approaches using large materials databases are useful for the analysis of energetics and stability of hundreds of thousands of compounds, but their utility for materials discovery is largely limited to idealized conditions of zero temperature and pressure. Here, we present a novel framework combining the two computational approaches, using a simple linear approximation to the enthalpy of a compound in conjunction with ambient-conditions data currently available in high-throughput databases of calculated materials properties. We demonstrate its utility by explaining the occurrence of phases in nature that are not ground states at ambient conditions and by estimating the pressures at which such ambient-metastable phases become thermodynamically accessible, as well as guiding the exploration of ambient-immiscible binary systems via sophisticated structural search methods to discover new high-pressure phases.

We solve a minimal model for an ergodic phase in a spatially extended quantum many-body system. The model consists of a chain of sites with nearest-neighbor coupling under Floquet time evolution. Quantum states at each site span a $q$-dimensional Hilbert space, and time evolution for a pair of sites is generated by a $q^2\times q^2$ random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbor on one side during the first half of the evolution period and to its neighbor on the other side during the second half of the period. We show how dynamical behavior averaged over realizations of the random matrices can be evaluated using diagrammatic techniques and how this approach leads to exact expressions in the large-$q$ limit. We give results for the spectral form factor, relaxation of local observables, bipartite entanglement growth, and operator spreading.

The thermal conductivity $\kappa$ of the cuprate superconductor ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ was measured down to 50 mK in seven crystals with doping from $p=0.12$ to $p=0.24$, both in the superconducting state and in the magnetic field-induced normal state. We obtain the electronic residual linear term ${\kappa }_0/T$ as $T\to 0$ across the pseudogap critical point $p^{\star }=0.23$. In the normal state, we observe an abrupt drop in ${\kappa }_0/T$ upon crossing below $p^{\star }$, consistent with a drop in carrier density $n$ from $1+p$ to $p$, the signature of the pseudogap phase inferred from the Hall coefficient. A similar drop in ${\kappa }_0/T$ is observed at $H=0$, showing that the pseudogap critical point and its signatures are unaffected by the magnetic field. In the normal state, the Wiedemann-Franz law, ${\kappa }_0/T=L_0/\rho (0)$, is obeyed at all dopings, including at the critical point where the electrical resistivity $\rho (T)$ is $T$ linear down to $T\to 0$. We conclude that the nonsuperconducting ground state of the pseudogap phase at $T=0$ is a metal whose fermionic excitations carry heat and charge as conventional electrons do.

We examine the problem of how excited populations of electrons relax after they have been excited by a pump. We include three of the most important relaxation processes: (i) impurity scattering, (ii) Coulomb scattering, and (iii) electron-phonon scattering. The relaxation of an excited population of electrons is one of the most fundamental processes measured in pump-probe experiments, but its interpretation remains under debate. We show how several common assumptions about nonequilibrium relaxation that are pervasive in the field may not hold under quite general conditions. The analysis shows that nonequilibrium relaxation is more complex than previously thought, but it yields to recently developed theoretical methods in nonequilibrium theory. In this work, we show how one can use many-body theory to properly interpret and analyze these complex systems. We focus much of the discussion on implications of these results for experiment.

The reflection of waves from rough surfaces is a fundamental process that plays a role in diverse fields such as optics, acoustics, and seismology. While a quantitative understanding of the reflection process has long been established for many types of waves, the precise manner in which thermal phonons of specific wavelengths reflect from atomically rough surfaces remains unclear owing to limited control over terahertz-frequency phonon generation and detection. Knowledge of these processes is critical for many applications, however, and is particularly important for recent attempts to create novel materials by coherently interfering thermal phonons. Here, we report measurements of a key property for these efforts, the phonon-wavelength-dependent specularity parameter, which describes the probability of specular reflections of thermal phonons at a surface. Our experiments show evidence of specular surface reflections of terahertz thermal phonons in our samples around room temperature and indicate a sensitivity of these reflections to surface imperfections on the scale of just 2–3 atomic planes. Our work demonstrates a general route to probe the microscopic interactions of thermal phonons with surfaces that are typically inaccessible with traditional experiments.

We report on an optically pumped laser where photons are simultaneously generated by population inversion and by stimulated Raman scattering in the same active medium, namely crystalline silicon doped by bismuth ($\mathrm{Si}:\mathrm{Bi}$). The medium utilizes three electronic levels: ground state [$|1⟩$: $1s(A_1)$ in $\mathrm{Si}:\mathrm{Bi}$], upper [$|3⟩$: $2p_{\pm }$] and lower [$|2⟩$: $1s(E)$] laser levels. The $|1⟩\leftrightarrow |3⟩$ and $|2⟩\leftrightarrow |3⟩$ transitions are optically allowed and the $|1⟩\leftrightarrow |2⟩$ transition is Raman active. Lasing based on population inversion occurs between the states $|3⟩$ and $|2⟩$, while Raman scattering benefits from the Raman-active transition. At high pump power the inversion-based stimulated emission $|3⟩\to |2⟩$ disappears, because electronic scattering from $|1⟩$ to $|2⟩$ via a virtual state dominates and the electrons are excited into $|2⟩$ rather than into $|3⟩$. Starting as population inversion-based lasing, it ends as stimulated Raman scattering. Our model shows that such a competition occurs on the timescale of the 10-ps-long pump pulse.

A remarkable recent experiment has observed Mott insulator and proximate superconductor phases in twisted bilayer graphene when electrons partly fill a nearly flat miniband that arises a “magic” twist angle. However, the nature of the Mott insulator, the origin of superconductivity, and an effective low-energy model remain to be determined. We propose a Mott insulator with intervalley coherence that spontaneously breaks $U(1)$ valley symmetry and describe a mechanism that selects this order over the competing magnetically ordered states favored by the Hund’s coupling. We also identify symmetry-related features of the nearly flat band that are key to understanding the strong correlation physics and constrain any tight-binding description. First, although the charge density is concentrated on the triangular-lattice sites of the moiré pattern, the Wannier states of the tight-binding model must be centered on different sites which form a honeycomb lattice. Next, spatially localizing electrons derived from the nearly flat band necessarily breaks valley and other symmetries within any mean-field treatment, which is suggestive of a valley-ordered Mott state, and also dictates that additional symmetry breaking is present to remove symmetry-enforced band contacts. Tight-binding models describing the nearly flat miniband are derived, which highlight the importance of further neighbor hopping and interactions. We discuss consequences of this picture for superconducting states obtained on doping the valley-ordered Mott insulator. We show how important features of the experimental phenomenology may be explained and suggest a number of further experiments for the future. We also describe a model for correlated states in trilayer graphene heterostructures and contrast it with the bilayer case.

We build symmetry-adapted maximally localized Wannier states and construct the low-energy tight-binding model for the four narrow bands of twisted bilayer graphene. We do so when the twist angle is commensurate near the “magic” value and the narrow bands are separated from the rest of the bands by energy gaps. On each layer and sublattice, every Wannier state has three peaks near the triangular moiré lattice sites. However, each Wannier state is localized and centered around a site of the honeycomb lattice that is dual to the triangular moiré lattice. The space group and the time-reversal symmetries are realized locally. The corresponding tight-binding model provides a starting point for studying the correlated many-body phases.

We develop an effective extended Hubbard model to describe the low-energy electronic properties of the twisted bilayer graphene. By using the Bloch states in the effective continuum model and with the aid of the maximally localized algorithm, we construct the Wannier orbitals and obtain an effective tight-binding model on the emergent honeycomb lattice. We find that the Wannier state takes a peculiar three-peak form in which the amplitude maxima are located at the triangle corners surrounding the center. We estimate the direct Coulomb interaction and the exchange interaction between the Wannier states. At the filling of two electrons per supercell, in particular, we find an unexpected coincidence in the direct Coulomb energy between a charge-ordered state and a homogeneous state, which could possibly lead to an unconventional many-body state.