Deconfined quantum critical points (DQCPs) are putative phase transitions beyond the Landau paradigm with emergent fractionalized degrees of freedom. The original example of a DQCP is the spin-$\frac{1}{2}$ quantum antiferromagnet on the square lattice which features a second-order transition between valence bond solid (VBS) and Néel order. The VBS order breaks a lattice symmetry, and the corresponding VBS order parameter may couple to lattice distortion modes (phonons) at appropriate momenta. We investigate a field-theoretic description of the DQCP in the presence of such a spin-lattice coupling. We show that treating phonons as classical lattice distortions leads to a relevant monopole-phonon interaction inducing an instability towards a distorted lattice by an analogous mechanism to the spin-Peierls instability in one dimension. Consequently, there is a breakdown of the DQCP which generally becomes a strong first-order transition. Taking into account the full quantum nature of the phonons, we argue that the continuous DQCP persists above a critical phonon frequency. Lastly, we comment on the connection to general gapless, deconfined gauge theories.

We construct and study the relativistic Gross-Neveu-Yukawa field theory for the $\text{SO}\left(2N\right)$ real symmetric second-rank tensor order parameter coupled to $N_f$ flavors of $4N$-component Majorana fermions in $2+1$ dimensions. Such a tensor order parameter unifies all Lorentz-invariant mass-gap orders for $N$ two-component Dirac fermions in two dimensions except for the $\text{SO}\left(2N\right)$-singlet anomalous quantum Hall state. The value $N_f=1$ corresponds to the canonical Gross-Neveu model. Within the leading-order $\epsilon$-expansion around the upper critical dimension of $3+1$, the field theory exhibits a critical fixed point in its renormalization group flow which describes spontaneous symmetry breaking to $\text{SO}\left(N\right)\times \text{SO}\left(N\right)$ for the number of flavors of Majorana fermions higher than a critical value $N_{f,c2}\approx 2N$. For $N_{f,c1}<N_f<N_{f,c2}$, with $N_{f,c1}\approx N$, the critical fixed point resides in the unstable region of the theory where the effective potential is unbounded from below, whereas for $N_f<N_{f,c1}$ there is no real critical fixed point and the flow runs away. In either case, for $N_f<N_{f,c2}$ the transition should become fluctuation-induced first order, and we discuss the dependence of its size on the parameters $N$ and $N_f$ in the theory. One-loop critical exponents for the universality class at $N_{f,c2}<N_f$ are computed and the flow diagram in various regimes is discussed.

Recently, a quantum simulator for the two-dimensional Fermi-Hubbard model on an anisotropic triangular lattice has been realized, where both geometrical frustration and doping can be continuously tuned. Here, we provide a comprehensive comparison between the magnetic correlations calculated by the two-particle self-consistent (TPSC) theory and those measured in this quantum simulator, at temperatures comparable to the spin-exchange energy and Hubbard interactions comparable to the bandwidth. We find overall excellent agreements between the TPSC calculations and the measurements from the quantum simulator at all levels of frustration and doping. This is quite remarkable considering that the Hubbard model is already in the intermediate- to strong-coupling regime, for which very few methods yield reliable results. Our work showcases the potential of TPSC as a theoretical approach capable of providing reasonably accurate descriptions of the Hubbard model even at fairly strong interactions and when the frustration is present.

We predict that an interplay between isotropic and anisotropic exchange interactions in a honeycomb lattice structure can lead to topological edge conduction when the anisotropic interaction is at least twice the strength of the isotropic interaction. For materials like ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, such a strong anisotropic exchange interaction simultaneously induces a zigzag type of antiferromagnetic order that breaks the time-reversal symmetry of the topological edge conductor. We show that the electronic transport in such topological conductors will exhibit a quantized Hall conductance without any external magnetic field when the Fermi energy lies within a particular energy range.

We construct a model that exhibits resistivity going as a power law in temperature $T$, as $T^{\alpha }$ down to the lowest temperature. There is no residual resistivity because we assume the absence of disorder and momentum relaxation is due to umklapp scattering. Our model consists of a quantum spin liquid state with a spinon Fermi surface and a hole Fermi surface made out of doped holes. The key ingredient is a set of singular $2k_F$ modes living on a ring in momentum space. Depending on parameters, $\alpha$ may be unity (strange metal) or even smaller. The model may be applicable to a doped organic compound, which has been found to exhibit linear $T$ resistivity. We conclude that it is possible to obtain strange metal behavior starting with a model that is not so strange.

We show that the continuum limit of moiré graphene is described by a $(2+1)$-dimensional field theory of Dirac fermions coupled to two classical vector fields: a periodic gauge and a spin field. We further show that the existence of a flat band implies an effective dimensional reduction, where the time dimension is “removed.” The resulting two-dimensional Euclidean theory contains the chiral anomaly. The associated Atiyah-Singer index theorem provides a self-consistency condition for flat bands. In the Abelian limit, where the spin field is disregarded, we reproduce a periodic series of quantized magic angles known to exist in twisted bilayer graphene in the chiral limit. However, the results are not exact. If the Abelian field has zero total flux, perfectly flat bands can not exist, because of the leakage of edge states into neighboring triangular patches with opposite field orientations. We demonstrate that the non-Abelian spin component can correct this and completely flatten the bands via an effective renormalization of the Abelian component into a configuration with a nonzero total flux. We present the Abelianization of the theory where the Abelianized flat band can be mapped to that of the lowest Landau level. We show that the Abelianization corrects the values of the magic angles consistent with numerical results. We also use this criterion to prove that an external magnetic field splits the series into pairs of magnetic field-dependent magic angles associated with flat moiré-Landau bands. The topological criterion and the Abelianization procedure provide a generic practical method for finding flat bands in a variety of material systems including but not limited to moiré bilayers.

The fascinating properties of unconventional Dirac and Weyl nodes in crystalline systems, carrying a topological charge of $\pm 2$, have captured the attention of researchers. Here, applying $k·p$ analysis, we demonstrate that space group 92 facilitates the emergence of charge-2 Dirac point and charge-2 Weyl point. Notably, the constructed phononic crystal is allowed to be a concise configuration containing only a charge-2 Dirac point and a charge-2 Weyl point in pairs appearing simultaneously, that is, the realization of the unconventional Dirac-Weyl semimetal (UDWS). The projected dispersion bands reveal the unique double helical surface arcs of UDWS, which alternate from the projected charge-2 Dirac point to the projected charge-2 Weyl point, spanning the entire Brillouin zone with ultralong trajectories. The unique global surface arc characteristic demonstrates robust resilience against defects, underscoring its suitability as an optimal platform for investigating ultralong surface arcs.

We report magnetic ground state, dynamical magnetic properties, and the spin Hamiltonian of the two-dimensional distorted ($J_1\text{−}{J}_2$) triangular lattice antiferromagnetic (TLAFM) spin-5/2 system $\mathrm{N}{\mathrm{a}}_3\mathrm{Fe}{\left(\mathrm{P}{\mathrm{O}}_4\right)}_2$ by neutron diffraction, inelastic neutron scattering (INS), and density-functional-theory (DFT) calculations. The compound $\mathrm{N}{\mathrm{a}}_3\mathrm{Fe}{\left(\mathrm{P}{\mathrm{O}}_4\right)}_2$ is characterized by distorted triangular lattice with two different nearest neighbor exchange interactions $J_1$ and $J_2$; and having a collinear stripy antiferromagnetic (AFM) ground state. The powder INS spectrum consists of two bands of magnetic excitations (over 0.25–2.0 and 3.0–5.5 meV) with a small energy gap of $\sim 0.25\mathrm{meV}$, a typical characteristic feature of spin-wave excitations of an ordered magnetic state. We model the experimentally observed features of magnetic excitations by linear spin-wave theory and determine the dominant in-plane magnetic exchange interactions $J_1=-0.31$ meV (FM), and $J_2=0.15$ meV (AFM). The values of the exchange interaction constants determined from the INS study and the DFT calculations are in good agreement. Further, the interplanar exchange interaction [$J_3=0.00003$ meV (AFM)] has been estimated to be negligible. By determining the spin Hamiltonian through experimental INS and DFT calculations, we could shed light on the microscopic origin of the collinear stripy AFM ground state and verify the theoretical predicted magnetic phase diagram. Besides, the in-depth calculation of first principles Wannier function provides the exchange interaction mechanism between magnetic Fe ions in $\mathrm{N}{\mathrm{a}}_3\mathrm{Fe}{\left(\mathrm{P}{\mathrm{O}}_4\right)}_2$. The present study provides an in-depth knowledge of magnetic ground state, their excitations and the spin-Hamiltonian of $\mathrm{N}{\mathrm{a}}_3\mathrm{Fe}{\left(\mathrm{P}{\mathrm{O}}_4\right)}_2$ which is helpful to understand the phase diagram of a distorted TLAFM system in general.

Relaxation time plays a crucial role in describing the relaxation processes of quantum systems. We study the effect of a type of bond dissipation on the relaxation time of boundary dissipative systems and find that it can change the scaling of the relaxation time $T_c\sim L^z$ from $z=3$ to a value significantly less than 3. We further reveal that the reason such bond dissipation can significantly reduce the relaxation time is that it can selectively target specific states. For Anderson-localized systems, the scaling behavior of the relaxation time changes from an exponential form to a power-law form as the system size varies. This is because the bond dissipation we consider can not only select specific states but can also disrupt the localization properties. Our work reveals that in open systems one type of dissipation can be used to regulate the effects produced by another type of dissipation.

We design a $(2+1)$-dimensional $\left[\right(2+1\left)\mathrm{D}\right]$ quantum spin model in which spin-1/2 ladders are coupled through antiferromagnetic Ising interactions. The model hosts a quantum phase transition in the $(2+1)\mathrm{D}$ $Z_2$ universality class from the Haldane phase to the antiferromagnetic Ising ordered phase. We focus on studying the surface properties of three different surface configurations when the Ising couplings are tuned. Different behaviors are found on different surfaces. We find ordinary and two different extraordinary surface critical behaviors (SCBs) at the bulk critical point. The ordinary SCBs belong to the surface universality class of the classical 3D Ising bulk transition. One extraordinary SCBs is induced by the topological properties of the Haldane phase. Another extraordinary SCBs at the bulk critical point is induced by an unconventional surface phase transition where the surface develops an Ising order before the bulk. This surface transition is realized by coupling a $(1+1)$-dimensional $\left[\right(1+1\left)\mathrm{D}\right]$ $SU{\left(2\right)}_1$ CFT boundary to a $(2+1)\mathrm{D}$ bulk with $Z_2$ symmetry. We find that the transition is neither a $(1+1)\mathrm{D}$ $Z_2$ transition, expected based on symmetry consideration, nor a Kosterlitz-Thouless-like transition, violating the previous theoretical prediction. This new surface phase transition and related extraordinary SCBs deserve further analytical and numerical exploration.

The recently discovered nonlinear Hall (NLH) effect arises either without external magnetic field (type-I) or with an in-plane magnetic field (type-II). In this work we propose a new type of geometrical nonlinear Hall effect with an out-of-plane magnetic field (type-III) induced by the combination of Lorentz force and anomalous electronic velocity. The type-III NLH effect is proportional to the more refined structures of Bloch wave functions, i.e., the dipole moment of square of Berry curvature, thus becoming prominent near the band crossings or anticrossings. Our effective model analysis and first-principles calculations show that gate-tuned ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ thin film under uniaxial strain is an ideal platform to observe this effect. Especially, giant unidirectional magnetoresistance can occur in this material, based on which an efficient electrical transistor device prototype can be built. Finally, a symmetry analysis indicates that type-III NLH effect has unique symmetry properties stemming from Berry curvature square dipole, which is different from other previously reported NLH effects and can exist in a wider class of magnetic crystals. Our study offers paradigms for nonlinear electronics.

Among the variational wave functions for fermionic Hamiltonians, neural network backflow (NNBF) and hidden fermion determinant states (HFDS) are two prominent classes that provide accurate approximations to the ground state. Here we develop a unifying view of fermionic neural quantum states casting them all in the framework of NNBF. NNBF wave functions have configuration-dependent single-particle orbitals (SPO) which are parameterized by a neural network. We show that HFDS can be written as a NNBF wave function with a restricted low-rank $r$ additive correction to the SPO times a neural-network generated determinant of an $r\times r$ matrix. Furthermore, we show that in NNBF wave functions, this $r\times r$ determinant can generically be removed when $r$ is less than or equal to the number of fermions, at the cost of further complicating the additive SPO correction increasing its rank by $r$. We numerically and analytically compare additive SPO corrections generated by the product of two matrices with inner dimension $r$. We find that larger $r$ wave functions span a larger space and give evidence that simpler and more direct updates to the SPO's tend to be more expressive and better energetically. These suggest the standard NNBF approach is preferred amongst other related choices. Finally, we uncover that the row selection used to select single-particle orbitals allows significant sign and amplitude modulation between nearby configurations and is partially responsible for the quality of NNBF and HFDS wave functions.

We present an analytic theory unraveling the microscopic mechanism of instabilities within interacting $D$-dimensional Fermi liquid. Our model consists of a $D$-dimensional electron gas subject to an instantaneous electron-electron interaction of a finite range exceeding the average interparticle distance. Pair, charge, and spin susceptibilities are evaluated via the one-loop renormalization group theory and via the bosonization approach, giving identical results. In case of a repulsive interaction, we identify an intrinsic Fermi-liquid instability towards insulating spin- and charge-density-wave order when the interaction coupling strength reaches a universal critical value. If both electron and hole pockets of the same size are present, the ground state is an excitonic insulator at arbitrarily small repulsive interaction. If the interaction is attractive, the ground state is a singlet non-BCS superconductor with a uniform condensate. In case if both electron and hole Fermi surfaces are present, we predict an instability towards the interpocket pair-density-wave ordering at the critical coupling. This prediction lends strong theoretical support to the pair-density-wave scenario of superconductivity in cuprate materials. Due to its simple and universal nature, presented microscopic mechanism of intrinsic instabilities of interacting $D$-dimensional Fermi liquids constitutes a solid theoretical ground for understanding quantum phase transitions in a variety of quantum materials, from ultraclean semiconductor quantum wells to high-temperature superconductors.

Control of doping and carrier concentration at the nanoscale is an essential requirement to realize future electronic and optoelectronic devices in two-dimensional van der Waals (vdW) heterostructures. In spite of great efforts on the related study, introducing nanoscale high-quality junctions with custom-designed sizes and sites remains an outstanding challenge in experiments. Here, we overcome the challenges by combining scanning tunneling microscope (STM) lithography with structural phase transition of transition metal dichalcogenides (TMDs). Our experiments demonstrate that nanoscale TMD islands can be created, moved, sliced, and merged at the interface of graphene/TMD heterostructures by using a STM tip. The reported method can in situ introduce the structural phase transition in the interfacial TMD islands, generating well-defined nanoscale electrostatic potentials in graphene and enabling the realization of custom-designed artificial model systems. Our result enables the creation of high-quality patterned quantum confined systems to fully engineer electronic and optoelectronic properties of vdW heterostructures.

With the aid of Keldysh nonequilibrium Green's functions, we investigate the quench dynamics in a superconductor–quantum dot–superconductor (S-QD-S) Josephson junction during transient transport processes going beyond the wide-band limit. We calculate the transient current when the bias is suddenly turned off/on. We find that because of the distinct physical mechanisms that govern superconducting current in zero-bias and nonzero-bias scenarios, the quench dynamics of the “turning-off” and “turning-on” transient processes exhibit significant differences. When the bias is turned off, aided by quasiparticle bound states, electrons become trapped in the energy gap and oscillate between the bound states $\pm {\epsilon }_b$. Consequently, the turning-off transient current exhibits oscillations at a frequency of $2{\epsilon }_b$, which is dependent on $\varphi$. Because the bound states in a $\varphi$-driven Josephson junction have an infinite lifetime, the turning-off transient current exhibits perpetual oscillations and relaxes towards the steady state at an infinitely slow rate. In contrast, the turning-on transient current, which is underpinned by multiple Andreev reflections, quickly settles into a steady alternating state at a frequency of $2V$. The infinite relaxation time of the turning-off transient current, in conjunction with the distinct quench dynamics observed during both “turning-off” and “turning-on” operations, reveals the unique role of quasiparticle trapping in superconducting transient transport processes.