In a typical quantum annealing protocol, the system starts with a transverse field Hamiltonian which is gradually turned off and replaced by a longitudinal Ising Hamiltonian. The ground state of the Ising Hamiltonian encodes the solution to the compu
tational problem of interest, and the state overlap with this ground state gives the success probability of the annealing protocol. The form of the annealing schedule can have a significant impact on the ground state overlap at the end of the anneal, so precise control over these annealing schedules can be a powerful tool for increasing success probabilities of annealing protocols. Here we show how superconducting circuits, in particular capacitively shunted flux qubits (CSFQs), can be used to construct quantum annealing systems by providing tools for mapping circuit flux biases to Pauli coefficients. We use this mapping to find customized annealing schedules: appropriate circuit control biases that yield a desired annealing schedule, while accounting for the physical limitations of the circuitry. We then provide examples and proposals that utilize this capability to improve quantum annealing performance.
The experimentally observed correlated insulating states and quantum anomalous Hall (QAH) effect in twisted bilayer graphene (TBG) have drawn significant attention. However, up to date, the specific mechanisms of these intriguing phenomena are still
open questions. Using a fully unrestricted Hartree-Fock variational method, we have explained the correlated insulating states and QAH effects at various integer fillings of the flat bands in TBG. Our results indicate that states breaking flavor (valley and spin) symmetries are energetically favored at all integer fillings. In particular, the correlated insulating states at $pm 1/2$ filling and at the charge neutrality point are all valley polarized sates which break $C_{2z}$ and time-reversal ($mathcal{T}$) symmetries, but preserves $C_{2z}mathcal{T}$ symmetry. Such valley polarized states exhibit moire orbital antiferromagnetic ordering on an emergent honeycomb lattice with compensating circulating current pattern in the moire supercell. Within the same theoretical framework, our calculations indicate that the $C!=!mp 1$ QAH states at $pm 3/4$ fillings of the magic-angle TBG are spin and orbital ferromagnetic states, which emerge when a staggered sublattice potential is present. We find that the nonlocalness of the exchange interactions tend to enhance the bandwidth of the low-energy bands due to the exchange-hole effect, which reduces the gaps of the correlated insulator phases. The nonlocal exchange interactions also dramatically enhance the spin polarization of the system, which significantly stabilize the orbital and spin ferromagnetic QAH state at $3/4$ filling of TBG aligned with hexagonal boron nitride (hBN). We also predict that, by virtue of the orbital ferromagnetic nature, the QAH effects at electron and hole fillings of hBN-aligned TBG would exhibit hysteresis loops with opposite chiralities.
We analyze the instability of an unpolarized uniform quantum plasma consisting of two oppositely charged fermionic components with varying mass ratios, against charge and spin density waves (CDWs and SDWs). Using density functional theory, we treat e
ach component with the local spin density approximation and a rescaled exchange-correlation functional. Interactions between different components are treated with a mean-field approximation. In both two- and three-dimensions, we find leading unstable CDW modes in the second-order expansion of the energy functional, which would induce the transition to quantum liquid crystals. The transition point and the length of the wave-vector are computed numerically. Discontinuous ranges of the wave-vector are found for different mass ratios between the two components, indicating exotic quantum phase transitions. Phase diagrams are obtained and a scaling relation is proposed to generalize the results to two-component fermionic plasmas with any mass scale. We discuss the implications of our results and directions for further improvement in treating quantum plasmas.
We study the anomalous Hall effect, magneto-optical properties, and nonlinear optical properties of twisted bilayer graphene (TBG) aligned with hexagonal boron nitride (hBN) substrate as well as twisted double bilayer graphene systems. We show that n
on-vanishing valley polarizations in twisted graphene systems would give rise to anomalous Hall effect which can be tuned by in-plane magnetic fields. The valley polarized states are also associated with giant Faraday/Kerr rotations in the terahertz frequency regime. Moreover, both hBN-aligned TBG and TDBG exhibit colossal nonlinear optical responses by virtue of the inversion-symmetry breaking, the small bandwidth, and the small excitation gaps of the systems. Our calculations indicate that in both systems the nonlinear optical conductivities of the shift currents are on the order of $10^3,mu$A/V$^2$; and the second harmonic generation (SHG) susceptibilities are on the order of $10^6,$pm/V in the terahertz frequency regime. Moreover, in TDBG with $ABtextrm{-}BA$ stacking, we find that a finite orbital magnetization would generate a new component $sigma^{x}_{xx} $ of the nonlinear photoconductivity tensor; while in $AB$-$AB$ stacked TDBG with vertical electric fields, the valley polarization and orbital magnetization would make significant contributions to the $sigma^{y}_{xx}$ component of the photoconductivity tensor. These nonlinear photo-conductivities are proportional to the orbital magnetizations of the systems, thus they are expected to exhibit hysteresis behavior in response to out-of-plane magnetic fields.
Quasiparticles and collective modes are two fundamental aspects that characterize a quantum matter in addition to its ground state features. For example, the low energy physics for Fermi liquid phase in He-III was featured not only by Fermionic quasi
particles near the chemical potential but also by fruitful collective modes in the long-wave limit, including several different sound waves that can propagate through it under different circumstances. On the other hand, it is very difficult for sound waves to be carried by the electron liquid in the ordinary metals, due to the fact that long-range Coulomb interaction among electrons will generate plasmon gap for ordinary electron density fluctuation and thus prohibits the propagation of sound waves through it. In the present paper, we propose a unique type of acoustic collective modes in Weyl semimetals under the magnetic field called chiral zero sound. The chiral zero sound can be stabilized under so-called chiral limit, where the intra-valley scattering time is much shorter than the inter-valley one, and only propagates along an external magnetic field for Weyl semimetals with multiple-pairs of Weyl points. The sound velocity of the chiral zero sound is proportional to the field strength in the weak field limit, whereas it oscillates dramatically in the strong field limit, generating an entirely new mechanism for quantum oscillations through the dynamics of neutral bosonic excitation, which may manifest itself in the thermal conductivity measurements under magnetic field.
We propose that the electronic structure of twisted bilayer graphene (TBG) can be understood as Dirac fermions coupled with opposite pseudo magnetic fields generated by the moire pattern. The two low-energy flat bands from each monolayer valley origi
nate from the two zeroth pseudo Landau levels of Dirac fermions under such opposite effective magnetic fields, which have opposite sublattice polarizations and carry opposite Chern numbers $pm1$, giving rise to helical edge states in the gaps below and above the low-energy bulk bands near the first magic angle. We argue that small Coulomb interactions would split the eight-fold degeneracy (including valley and physical spin) of these zeroth pseudo Landau levels, and may lead to insulating phases with non-vanishing Chern numbers at integer fillings. Besides, we show that all the high-energy bands below or above the flat bands are also topologically nontrivial in the sense that for each valley the sum of their Berry phases is quantized as $pmpi$. Such quantized Berry phases give rise to nearly flat edge states, which are dependent on truncations on the moire length scale. Our work provides a complete and clear picture for the electronic structure and topological properties of TBG, and has significant implications on the natrue of the correlated insulating phase observed in experiments.
We review the recent, mainly theoretical, progress in the study of topological nodal line semimetals in three dimensions. In these semimetals, the conduction and the valence bands cross each other along a one-dimensional curve in the three-dimensiona
l Brillouin zone, and any perturbation that preserves a certain symmetry group (generated by either spatial symmetries or time-reversal symmetry) cannot remove this crossing line and open a full direct gap between the two bands. The nodal line(s) is hence topologically protected by the symmetry group, and can be associated with a topological invariant. In this Review, (i) we enumerate the symmetry groups that may protect a topological nodal line; (ii) we write down the explicit form of the topological invariant for each of these symmetry groups in terms of the wave functions on the Fermi surface, establishing a topological classification; (iii) for certain classes, we review the proposals for the realization of these semimetals in real materials and (iv) we discuss different scenarios that when the protecting symmetry is broken, how a topological nodal line semimetal becomes Weyl semimetals, Dirac semimetals and other topological phases and (v) we discuss the possible physical effects accessible to experimental probes in these materials.
We have given a summary on our theoretical predictions of three kinds of topological semimetals (TSMs), namely, Dirac semimetal (DSM), Weyl semimetal (WSM) and Node-Line Semimetal (NLSM). TSMs are new states of quantum matters, which are different wi
th topological insulators. They are characterized by the topological stability of Fermi surface, whether it encloses band crossing point, i.e., Dirac cone like energy node, or not. They are distinguished from each other by the degeneracy and momentum space distribution of the nodal points. To realize these intriguing topological quantum states is quite challenging and crucial to both fundamental science and future application. In 2012 and 2013, Na$_3$Bi and Cd$_3$As$_2$ were theoretically predicted to be DSM, respectively. Their experimental verifications in 2014 have ignited the hot and intensive studies on TSMs. The following theoretical prediction of nonmagnetic WSM in TaAs family stimulated a second wave and many experimental works have come out in this year. In 2014, a kind of three dimensional crystal of carbon has been proposed to be NLSM due to negligible spin-orbit coupling and coexistence of time-reversal and inversion symmetry. Though the final experimental confirmation of NLSM is still missing, there have been several theoretical proposals, including Cu$_3$PdN from us. In the final part, we have summarized the whole family of TSMs and their relationship.
The electronic structure and magnetic properties of the strongly correlated material La$_2$O$_3$Fe$_2$Se$_2$ are studied by using both the density function theory plus $U$ (DFT+$U$) method and the DFT plus Gutzwiller (DFT+G) variational method. The g
round-state magnetic structure of this material obtained with DFT+$U$ is consistent with recent experiments, but its band gap is significantly overestimated by DFT+$U$, even with a small Hubbard $U$ value. In contrast, the DFT+G method yields a band gap of 0.1 - 0.2 eV, in excellent agreement with experiment. Detailed analysis shows that the electronic and magnetic properties of of La$_2$O$_3$Fe$_2$Se$_2$ are strongly affected by charge and spin fluctuations which are missing in the DFT+$U$ method.
In this article, we will give a brief introduction to the topological insulators. We will briefly review some of the recent progresses, from both theoretical and experimental sides. In particular, we will emphasize the recent progresses achieved in China.
