J. Bobroff, N. Laflorencie, L. K. Alexander, A. V. Mahajan, B. Koteswararao, P. Mendels
In this supplementary material, we investigate further the impurity-induced freezing mechanism in a doped system of 3D weakly coupled ladders resembling Bi(Cu$_{1-x}$Zn$_x$)$_2$ZnPO$_6$ using large scale Quantum Monte Carlo simulations.
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To understand the impurity effect on Tc in FeAs superconductors, we analyze a simple two-band BCS model with repulsive interband interaction. The realized fully-gapped superconducting state with sign reversal, which is predicted by spin fluctuation theories in this compound, is suppressed by impurities due to the interband hopping of Cooper pairs, if the interband impurity scattering $I'$ is equal to the intraband one $I$. When $|I'/I| < 1$, in highly contrast, Tc is almost unchanged by strong impurity scattering since the interband scattering is almost prohibited by the multiple scattering ef…
The electron states of gapped pseudospin-1 fermions of the $α-{\cal T}_3$ lattice in the Coulomb field of a charged impurity are studied. The free $α-{\cal T}_3$ model has three dispersive bands with two energy gaps between them depending on the parameter $Θ$ which controls the coupling of atoms of honeycomb lattice with atoms in the center of each hexagon, thus, interpolating between graphene $Θ=0$ and the dice model $Θ=π/4$. The middle band becomes flat one with zero energy in the dice model. The bound electron states are found in the two cases: the centrally symmetric potential well and a r…
We have studied the effect of non-magnetic Zn impurities in the coupled spin-ladder Bi(Cu1xZnx)2PO6 using 31P NMR, muSR and Quantum Monte Carlo simulations. Our results show that the impurities induce in their vicinity antiferromagnetic polarizations, extending over a few unit cells. At low temperature, these extended moments freeze in a process which is found universal among various other spin-gapped compounds: isolated ladders, Haldane or Spin-Peierls chains. This allows us to propose a simple common framework to explain the generic low-temperature impurity induced freezings observed in low …
Detecting symmetry fractionalization in gapped quantum spin liquids by magnetic impurities
本文提出通过在高对称性位置放置自旋-1/2磁性杂质，利用近藤屏蔽区域中受晶体对称性保护的非Kramers双重态来探测有能隙Z2自旋液体中的对称性分数化，并用严格可解模型和大N理论加以证明。
Quantum impurity models are the prototypical examples of quantum many-body dynamics which manifests in their spectral and transport properties. Single channel Anderson(and Kondo model) leads to the Fermi liquid ground state in the strong coupling regime which corresponds to a stable infrared fixed point at which the quantum impurity gets completely screened by the conduction electrons. Quantum impurity models with non-trivial density of states exhibit quantum phase transition and this quantum criticality lies in the universality class of local quantum critical systems. In this paper, we report…
Topology and Quantum-Spin-Classical-Spin Crossover of the Gapped Kondo Effect
该研究结合Lanczos变换与自洽组态相互作用方案，数值探究带隙近藤效应的局域相图，利用三类拓扑不变量表征不同相，分析量子与经典杂质自旋间的交叉及相关近藤效应的特征。
We discuss the universal theory of localized impurities in the paramagnetic state of 2D antiferromagnets where the spin gap is assumed to be significantly smaller than a typical exchange energy. We study the impurity spin susceptibility near the host quantum transition from a gapped paramagnet to a Neel state, and we compute the impurity-induced damping of the spin-1 mode of the gapped antiferromagnet. Under suitable conditions our results apply also to d-wave superconductors.
Impurities in superconductors and their induced bound states are important both for engineering novel states such as Majorana zero-energy modes and for probing bulk properties of the superconducting state. The high-temperature cuprates offer a clear advantage in a much larger superconducting order parameter, but the nodal energy spectrum of a pure $d$-wave superconductor only allows virtual bound states. Fully gapped $d$-wave superconducting states have however been proposed in several cuprate systems thanks to subdominant order parameters producing $d+is$- or $d+id'$-wave superconducting stat…
We study a spin-1/2 Kondo impurity coupled to an unconventional host in which the density of band states vanishes either precisely at (``gapless'' systems) or on some interval around the Fermi level (``gapped''systems). Despite an essentially nonlinear band dispersion, the system is proven to exhibit hidden integrability and is diagonalized exactly by the Bethe ansatz.
We have investigated the finite temperature dynamics of the singlet to doublet continuous quantum phase transition in the gapped Anderson impurity model using hybridization expansion continuous time quantum Monte-Carlo. Using the self-energy and the longitudinal static susceptibility, we obtain a phase diagram in the temperature-gap plane. The separatrix between the low temperature local moment phase and the high temperature generalized Fermi liquid phase of this phase diagram is shown to be the lower bound of the critical scaling region of the zero gap quantum critical point of interacting ty…
We consider an Anderson impurity model in which the locally correlated orbital is coupled to a host with a gapped density of states. Single-particle dynamics are studied, within a perturbative framework that includes both explicit second-order perturbation theory and self-consistent perturbation theory to all orders in the interaction. Away from particle-hole symmetry the system is shown to be a generalized Fermi liquid (GFL) in the sense of being perturbatively connectable to the non-interacting limit; and the exact Friedel sum rule for the GFL phase is obtained. We show by contrast that the …
Low dimensional spin-1/2 systems with antiferromagnetic interactions display very innovative features, driven by strong quantum fluctuations. In particular, geometrical effects or competing magnetic interactions can give rise to the formation of a spin gap between the singlet ground state and the first excited triplet state. In this chapter, we focus on the numerical investigation of such systems by Exact Diagonalisation methods and some extensions of it including a simultaneous mean-field treatment of some perturbative couplings. After a presentation of the Lanczos algorithm and a description…
Probing frustrated spin systems with impurities
研究通过杂质相互作用探测反铁磁自旋系统，揭示了弱耦合和强耦合区域的不同相互作用行为，区分了无隙和有隙相。
Rigorous Wilsonian Renormalization Group for impurity models with a spectral gap
本文提出对数隙数值RG方法，通过隙边缘累积离散化和交替对角化，统一处理超导与标量带隙安德森杂质模型，并首次精确求解带隙AIM。
Magnetic phase transition under hydrostatic pressure in TlCu$_{0.988}$Mg$_{0.012}$Cl$_3$ was investigated by magnetization measurements. The parent compound TlCuCl$_3$ is a coupled spin dimer system, which undergoes a pressure-induced quantum phase transition from a gapped ground state to an antiferromagnetic state at $P_{\rm c} = 0.42$ kbar due to the shrinkage of the gap. At ambient pressure, the present doped system exhibits impurity-induced magnetic ordering at $T_{\rm N}=2.5$ K. With increasing pressure, $T_{\rm N}$ increases. This is because the effective exchange interaction $J_{\rm eff…
We study the distribution of vacuum polarization charge induced by a Coulomb impurity in massive graphene. By analytically computing the polarization function, we show that the charge density is distributed in space in a non-trivial fashion, and on a characteristic length-scale set by the effective Compton wavelength. The density crosses over from a logarithmic behavior below this scale, to a power law variation above it. Our results in the continuum limit are confirmed by explicit diagonalization of the corresponding tight-binding model on a finite-size lattice. Electron-electron interaction …
Geometrical frustration, quantum entanglement and disorder may prevent long-range order of localized spins with strong exchange interactions, resulting in a novel state of matter. $κ$-(BEDT-TTF)$_2$-Cu$_2$(CN)$_3$ is considered the best approximation of this elusive quantum-spin-liquid state, but its ground-state properties remain puzzling. Here we present a multi-frequency electron-spin resonance study down to millikelvin temperatures, revealing a rapid drop of the spin susceptibility at $T^*=6\,\mathrm{K}$. This opening of a spin gap, accompanied by structural modifications, suggests the eni…
We reveal a new type of supercritical behavior in gapped graphene with two oppositely charged impurities by studying the two-dimensional Dirac equation for quasiparticles with the Coulomb potential regularized at small distances accounting the lattice effects. By utilizing the variational Galerkin--Kantorovich method, we show that for supercritical electric dipole the wave function of the electron bound state changes its localization from the negatively charged impurity to the positively charged one as the distance between the impurities changes. Such a migration of the wave function correspon…
We study the superconducting state in newly discovered high-Tc superconductor K$_x$Fe$_2$Se$_2$ based on the ten-orbital Hubbard-Holstein model without hole-pockets. When the Coulomb interaction is large, spin-fluctuation mediated d-wave state appears due to the nesting between electron-pockets. Interestingly, the symmetry of the body-centered tetragonal structure in K$_x$Fe$_2$Se$_2$ requires the existence of nodes in the d-wave gap, although fully-gapped d-wave state is realized in the case of simple tetragonal structure. In the presence of moderate electron-phonon interaction due to Fe-ion …
The sign-reversing fully gapped superconducting state, which is expected to be realized in oxypnictide superconductors, can be prominently affected by nonmagnetic impurities due to the interband scattering of Cooper pairs. We study this problem based on the isotropic two-band BCS model: In oxypnictide superconductors, the interband impurity scattering $I'$ is not equal to the intraband one $I$. In the Born scattering regime, the reduction in Tc is sizable and the impurity-induced density of states (DOS) is prominent if $I\sim I'$, due to the interband scattering. Although impurity-induced DOS …
Gapped magnetic ground state in the spin-liquid candidate $κ$-(BEDT-TTF)$_2$Ag$_2$(CN)$_3$ suggested by magnetic spectroscopy
通过磁谱学研究，发现κ-(BEDT-TTF)₂Ag₂(CN)₃在低温下存在自旋单态关联和自旋能隙，同时存在杂质自旋贡献。
Using the density matrix renormalization group (DMRG) method, we study the quantum coherence in one-dimensional disordered Fermi systems. We consider in detail spinless fermions on a ring, and compare the influence of several kinds of impurities in a gapless and a dimerized, gapped system. In the translation-invariant system a so-called site-impurity, which can be realized by a local potential or a change of one link, increases for repulsive interaction and decreases for attractive interaction. The weakening of two neighboring bonds, which is a realization of a so-called bond-impurity, on the …
We investigate the interband and intraband transition of the monolayer and AB-stacked bilayer silicene in low-energy tight-binding model under the electric field, where we focus on the dynamical polarization function, screening due to the charged impurity, and the plasmon dispersion. We obtain the logarithmically divergen polarization function within the random-phase-approximation (RPA) whose logarithmic singularities corresponds to the discontinuities of the first derivative which is at the momentum ${\bf q}=2{\bf k}_{F}$ in static case and indicate the topological phase transition point from…
We construct a new class of edge theories for a family of fermionic Abelian topological phases with $K$-matrices of the form $K = \begin{pmatrix} k_1 & 0 \\ 0 & - k_2 \end{pmatrix}$, where $k_1, k_2 > 0$ are odd integers. Our edge theories are notable for two reasons: (i) they have finite dimensional Hilbert spaces (for finite sized systems) and (ii) depending on the values of $k_1, k_2$, some of the edge theories describe boundaries that cannot be gapped by any local interaction. The simplest example of such an ungappable boundary occurs for $(k_1, k_2) = (1, 3)$, which is realized by the $ν=…
We report the magnetic susceptibility and NMR studies of a spin-gapped layered compound Na2Cu2TeO6 (the spin gap $Δ\sim$ 250 K), the hole doping effect on the Cu2TeO6 plane via a topochemical Na deficiency by soft chemical treatment, and the static spin vacancy effect by nonmagnetic impurity Zn substitution for Cu. A finite Knight shift at the $^{125}$Te site was observed for pure Na2Cu2TeO6. The negative hyperfine coupling constant $^{125}A_{tr}$ is an evidence for the existence of a superexchange pathway of the Cu-O-Te-O-Cu bond. It turned out that both the Na deficiency and Zn impurities in…
We investigated the magnetic ground state and low-energy excitations of the spin chains compounds SrCuO$_{2}$ (zigzag chains) and Sr$_{2}$CuO$_{3}$ (linear chains) in the presence of quantum impurities induced by lightly doping ($\leq 1 \%$) with Zn$^{2+}$ ($S = 0$), Co$^{2+}$ ($S =1/2$) and Ni$^{2+}$ ($S = 1$) impurities at the Cu$^{2+}$ site. We show that the ground states and the nature of low-lying excitations (i.e., gapped or gapless) depend on the spin state and symmetry of the defects. For Ni doped chains a spin gap is observed but for Zn and Co doping the excitations remain gapless. Co…
The contribution to the entanglement of an impurity attached to one end of a $J-J_2-delta$ quantum spin chain (S=1/2) is studied. Two different measures of the impurity contribution to the entanglement have been proposed: the impurity-entanglement-entropy S_{imp} and the negativity N. The first, S_{imp}, is based on a subtractive procedure where the entanglement-entropy in the absence of the impurity is subtracted from results with the impurity present. The other, N, is the negativity of a part of the system separated from the impurity and the impurity itself. In this paper we compare the two …
Edge modes and boundary impurities in the anisotropic Heisenberg spin chain
本文利用Bethe Ansatz、精确对角化和DMRG系统研究了有能隙XXZ-1/2自旋链中边缘自旋-1/4模式与边界自旋-1/2杂质耦合的相图，揭示出Kondo相、反铁磁束缚模式相及不可积反铁磁耦合下的中隙激发相等多种相，深化了对分数化边缘模式下杂质屏蔽机制的理解。
Direct Evidence of Unconventional Superconductivity in Doped Kagome system RV$_3$Sb$_5$
该研究利用杂质束缚态光谱研究最优掺杂RbV₃Sb₅，发现其超导态为全能隙且具双能量尺度，证明其非常规手性超导性，确立了该光谱技术作为笼目材料超导的相位敏感探针。
We revisit the problem of a single quantum impurity on the edge of a two-dimensional time-reversal invariant topological insulator and show that the zero temperature phase diagram contains a large local moment region for antiferromagnetic Kondo coupling which was missed by previous poor man's scaling treatments. The combination of an exact solution at the so-called decoupling point and a renormalization group analysis à la Anderson-Yuval-Hamann allows us to access the regime of strong electron-electron interactions on the edge and strong Kondo coupling. We apply similar methods to the problem …
TlCuCl$_3$ is a coupled spin dimer system, which has a singlet ground state with an excitation gap of $Δ/gμ_{\mathrm B}$ = 5.5 T. TlCu$_{1-x}$Mg$_x$Cl$_3$ doped with nonmagnetic Mg$^{2+}$ ions undergoes impurity-induced magnetic ordering. Because triplet excitation with a finite gap still remains, this doped system can also undergo magnetic-field-induced magnetic ordering. By specific heat measurements and neutron scattering experiments under a magnetic field, we investigated the phase diagram in TlCu$_{1-x}$Mg$_x$Cl$_3$ with $x\sim 0.01$, and found that impurity- and field-induced ordered pha…
We study the interplay between disorder and interactions for emergent bosonic degrees of freedom induced by an external magnetic field in the Br-doped spin-gapped antiferromagnetic material Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ (DTNX). Building on nuclear magnetic resonance experiments at high magnetic field [A. Orlova et al., Phys. Rev. Lett. 118, 067203 (2017)], we describe the localization of isolated impurity states, providing a realistic theoretical modeling for DTNX. Going beyond single impurity localization we use quantum Monte Carlo simulations to explore many-body effects from whic…
Quantum spin-orbital liquids are elusive strongly correlated states of matter that emerge from quantum frustration between spin and orbital degrees of freedom. A promising route towards the observation of those states is the creation of artificial Mott insulators where antiferromagnetic correlations between spins and orbitals can be designed. We show that Coulomb impurity lattices on the surface of gapped honeycomb substrates, such as graphene on SiC, can be used to simulate SU(4) symmetric spin-orbital lattice models. We exploit the property that massive Dirac fermions form mid-gap bound stat…
Under the hydrostatic pressure $P=1.48$ GPa, polarized neutron elastic scattering experiments have been carried out on the coupled spin dimer system TlCuCl$_3$ with the gapped ground state at ambient pressure. Pressure-induced magnetic ordering occurs at the transition temperature $T_{\rm N}=16.9$ K. As in the field-induced and impurity-induced magnetic ordered phases, the ordered moments lie in the $a-c$ plane just below $T_{\rm N}$. An additional spin reorientation (SR) phase transition was observed at $T_{\rm SR}=10$ K, where the ordered moments start to incline toward the b-axis. The tempe…
We have investigated the dilute magnetic impurity effect on the magnetic properties of a quantum spin liquid candidate Ba3ZnRu2O9 and a spin gapped compound Ba3CaRu2O9. The magnetic ground state of each compound stands against 2% substitution of magnetic impurities for Zn or Ca. We have found that the magnetic response of these impurities, which behave as paramagnetic spins, depends on the host materials and the difference of the two manifests itself in the Weiss temperature, which can hardly be explained by the dilute magnetic impurities alone in the case of Ba3ZnRu2O9. We consider a contribu…
Fidelity of the Kitaev honeycomb model under a quench
本研究通过Kitaev蜂窝模型统一分析淬火扰动对量子态保真度的影响，发现能隙决定衰减行为，并给出普适长时保真度形式，为量子器件稳定性提供工程指导。
Thermodynamics in a split Hilbert space: Quantum impurity at the edge of a one-dimensional superconductor
本文研究一维超导体边缘单个磁性杂质的热力学，揭示其四个相（Kondo、YSR I/II、局域磁矩）的熵与自由能行为，并通过希尔伯特空间激发塔分裂给出超越传统TBA的闭式解析表达式。
Spectral properties of fractionalized Shiba states
本文研究BCS超导体中磁性杂质诱导的Shiba态，推广至一维分数化超导体，发现杂质仅耦合自旋并诱导量子相变，零温隧穿谱呈指数-1/2的普适幂律标度，有限温度下临界点谱特征仍具普适性。
The role of various magnetic inter-chain couplings has been investigated recently by numerical methods in doped frustrated quantum spin chains. A non-magnetic dopant introduced in a gapped spin chain releases a free spin-1/2 soliton. The formation of a local magnetic moment has been analyzed in term of soliton confinement. A four-spin coupling which might originate from cyclic exchange is shown to produce such a confinement. Dopants on different chains experience an effective space-extended non-frustrating pairwise spin interaction. This effective interaction between impurity-spins is long-ran…
We study the entanglement of an impurity at one end of a spin chain with a block of spins using negativity as a true measure of entanglement to characterize the unique features of the gapless Kondo regime in the spin chain Kondo model. For this spin chain in the Kondo regime we determine- with a true entanglement measure- the spatial extent of the Kondo screening cloud, we propose an ansatz for its ground state and demonstrate that the impurity spin is indeed maximally entangled with the cloud. To better evidence the peculiarities of the Kondo regime, we carry a parallel analysis of the entang…
Spin excitations are explored in the electron-doped spin-orbit Mott insulator (Sr$_{1-x}$La$_{x}$)$_3$Ir$_2$O$_7$. As this bilayer square lattice system is doped into the metallic regime, long-range antiferromagnetism vanishes, yet a spectrum of gapped spin excitation remains. Excitation lifetimes are strongly damped with increasing carrier concentration, and the energy integrated spectral weight becomes nearly momentum independent as static spin order is suppressed. Local magnetic moments, absent in the parent system, grow in metallic samples and approach values consistent with one $J=\frac{1…
Multichannel Kondo Effect in Superconducting Leads
研究了超导电极中多通道Kondo效应，揭示了强相关和能隙存在时的临界行为及不同相的特征。
Spin susceptibility of Anderson impurities is a key quantity in understanding the physics of Kondo screening. Traditional numerical renormalization group (NRG) calculation of the impurity contribution $χ_{\textrm{imp}}$ to susceptibility, defined originally by Wilson in a flat wide band, has been generalized before to structured conduction bands. The results brought about non-Fermi-liquid and diamagnetic Kondo behaviors in $χ_{\textrm{imp}}$, even when the bands are not gapped at the Fermi energy. Here, we use the full density-matrix (FDM) NRG to present high-quality data for the local suscept…
Magnetic-field-induced phase transitions are investigated in the frustrated gapped quantum paramagnet Rb$_{2}$Cu$_{2}$Mo$_3$O$_{12}$ through dielectric and calorimetric measurements on single-crystal samples. It is clarified that the previously reported dielectric anomaly at 8~K in powder samples is not due to a chiral spin liquid state as has been suggested, but rather to a tiny amount of a ferroelectric impurity phase. Two field-induced quantum phase transitions between paraelectric and paramagnetic and ferroelectric and magnetically ordered states are clearly observed. It is shown that the …
Quantum magnetic properties in a geometrically frustrated lattice of spin-1/2 magnet, such as quantum spin liquid or solid and the associated spin fractionalization, are considered key in developing a new phase of matter. The feasibility of observing the quantum magnetic properties, usually found in geometrically frustrated lattice of spin-1/2 magnet, in a perovskite material with controlled disorder is demonstrated. It is found that the controlled chemical disorder, due to the chemical substitution of Ru ions by Co-ions, in a simple perovskite CaRuO3 creates a random prototype configuration o…
Dynamics of one-dimensional spin models via complex-time evolution of tensor networks
本文将张量网络复时间演化用于一维 TFIM 与 XXZ 自旋模型，在抑制纠缠增长的同时重现实时动力学结果。
Motivated by the observation of unusual magnetism in Ce_xCu_2Si_2 ($x\sim 1$), we study the effect of disorder, such as Ce vacancy, on the competition between superconductivity (SC) and antiferromagnetism (AF) on the basis of the phenomenological Ginzburg-Landau theory. Assuming that the AF-SC transition is of first order in clean system, we show that a single impurity in the SC state can induce staggered magnetization by suppressing the SC around it. For finite concentration of impurities, the first-order AF-SC boundary in the clean case is replaced by a finite region where the SC and the ind…
Identifying Universal Spin Excitations in Spin-1/2 Kagome Quantum Spin Liquid Materials
本文通过高分辨率非弹性中子散射研究Zn-barlowite，发现其自旋激发谱与herbertsmithite一致，并结合密度矩阵重整化群计算确认了Kagome量子自旋液体基态及普适自旋子激发。
We determine the local density of states (LDOS) for spin-gapped one-dimensional charge density wave (CDW) states and Mott insulators in the presence of a hard-wall boundary. We calculate the boundary contribution to the single-particle Green function in the low-energy limit using field theory techniques and analyze it in terms of its Fourier transform in both time and space. The boundary LDOS in the CDW case exhibits a singularity at momentum 2kF, which is indicative of the pinning of the CDW order at the impurity. We further observe several dispersing features at frequencies above the spin ga…
The magnetic responses of a spin-1/2 ladder doped with non-magnetic impurities are studied using various methods and including the regime where frustration induces incommensurability. Several improvements are made on the results of the seminal work of Sigrist and Furusaki [J. Phys. Soc. Jpn. 65, 2385 (1996)]. Deviations from the Brillouin magnetic curve due to interactions are also analyzed. First, the magnetic profile around a single impurity and effective interactions between impurities are analyzed within the bond-operator mean-field theory and compared to density-matrix renormalization gro…
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