arXiv subjects

Guang-Ming Zhang

Publications and source records attributed to Guang-Ming Zhang.

At least 55 records · Page 3Linked to original sources

arXiv2020

Distinct pairing symmetries of superconductivity in infinite-layer nickelates

We report theoretical predictions on the pairing symmetry of the newly discovered superconducting nickelate Nd$_{1-x}$Sr$_{x}$NiO$_{2}$ based on the renormalized mean-field theory for a generalized model Hamiltonian proposed in [Phys. Rev. B \textbf{101}, 020501(R)]. For practical values of the key parameters, we find a transition between a gapped ($d+is$)-wave pairing state in the small doping region to a gapless $d$-wave pairing state in the large doping region, accompanied by an abrupt Fermi surface change at the critical doping. Our overall phase diagram also shows the possibility of a ($d+is$)- to $s$-wave transition if the electron hybridization is relatively small. In either case, the low-doping ($d+is$)-wave state is a gapped superconducting state with broken time-reversal symmetry. Our results are in qualitative agreement with recent experimental observations and predict several key features to be examined in future measurements.

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arXiv2020

Universal behavior of the thermal Hall conductivity

We report theoretical and experimental analyses of the thermal Hall conductivity in correlated systems. For both fermionic and bosonic excitations with nontrivial topology, we show that at "intermediate" temperatures, the thermal Hall conductivity exhibits an unexpected universal scaling with a simple exponential form. At low temperatures, it behaves differently and reflects the spectral properties of underlying excitations. Our predictions are examined as examples in two prototype compounds, the quantum paraelectric SrTiO$_3$ and the spin-liquid compound RuCl$_3$. The experimental data can be largely covered by our proposed minimal phenomenological model independent of microscopic details, revealing dominant bosonic contributions in SrTiO$_3$ and gapped fermionic excitations in RuCl$_3$. Our work establishes a phenomenological link between microscopic models and experimental data and provides a unified basis for analyzing the thermal Hall conductivity in correlated systems over a wide temperature region.

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arXiv2020

Dynamical spin excitations of topological Haldane gapped phase in the $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy

We study the dynamical spin excitations of the one-dimensional $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy by using quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation function. Using the transverse dynamic spin structure factor, we observe the quantum phase transition with a critical point between the topological Haldane gapped phase and the trivial phase. At the quantum critical point, we find a broad continuum characterized by the Tomonaga-Luttinger liquid similar to a $S=1/2$ Heisenberg antiferromagnetic chain. We further identify that the elementary excitations are fractionalized spinons.

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arXiv2020

Metal-to-metal transition and heavy-electron state in Nd$_4$Ni$_3$O$_{10-δ}$

The trilayer nickelate Nd$_4$Ni$_3$O$_{10-δ}$ ($δ\approx$ 0.15) was investigated by the measurements of x-ray diffraction, electrical resistivity, magnetic susceptibility, and heat capacity. The crystal structure data suggest a higher Ni valence in the inner perovskite-like layer. At ambient pressure the resistivity shows a jump at 162 K, indicating a metal-to-metal transition (MMT). The MMT is also characterized by a magnetic susceptibility drop, a sharp specific-heat peak, and an isotropic lattice contraction. Below $\sim$ 50 K, a resistivity upturn with a log$T$ dependence shows up, accompanying with a negative thermal expansion. External hydrostatic pressure suppresses the resistivity jump progressively, coincident with the diminution of the log$T$ behavior. The low-temperature electronic specific-heat coefficient is extracted to be $\sim$ 150 mJ K$^{-2}$ mol-fu$^{-1}$, equivalent to $\sim$ 50 mJ K$^{-2}$ mol-Ni$^{-1}$, indicating an unusual heavy-electron correlated state. The novel heavy-electron state as well as the logarithmic temperature dependence of resistivity is explained in terms of the Ni$^{3+}$ centered Kondo effect in the inner layer of the (NdNiO$_3$)$_3$ trilayers.

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arXiv2020

Tensor network approach to phase transitions of a non-Abelian topological phase

The non-abelian topological phase with Fibonacci anyons minimally supports universal quantum computation. In order to investigate the possible phase transitions out of the Fibonacci topological phase, we propose a generic quantum-net wavefunction with two tuning parameters dual with each other, and the norm can be exactly mapped into a partition function of the two-coupled $ϕ^{2}$-state Potts models, where $ϕ=(\sqrt{5}+1)/2$ is the golden ratio. By developing the tensor network representation of this wavefunction on a square lattice, we can accurately calculate the full phase diagram with the numerical methods of tensor networks. More importantly, it is found that the non-abelian Fibonacci topological phase is enclosed by three distinct non-topological phases and their dual phases of a single $ϕ^{2}$-state Potts model: the gapped dilute net phase, critical dense net phase, and spontaneous translation symmetry breaking gapped phase. We also determine the critical properties of the phase transitions among the Fibonacci topological phase and those non-topological phases.

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arXiv2019

Self-doped Mott insulator for parent compounds of nickelate superconductors

We propose the parent compound of the newly discovered superconducting nickelate Nd$_{1-x}$Sr$_{x}$NiO$_{2}$ as a self-doped Mott insulator, in which the low-density Nd-$5d$ conduction electrons couple to localized Ni-3$% d_{x^{2}-y^{2}}$ electrons to form Kondo spin singlets at low temperatures. This proposal is motivated with our analyses of the reported resistivity and Hall coefficient data in the normal state, showing logarithmic temperature dependence at low temperatures. In the strong Kondo coupling limit, we derive a generalized $t$-$J$ model with both Kondo singlets and nickel holons moving through the lattice of otherwise nickel spin-1/2 background. The antiferromagnetic long-range order is therefore suppressed as observed in experiments. With Sr-doping, the number of holons on the nickel sites increases, giving rise to the superconductivity and a strange metal phase analogous to those in superconducting copper oxides.

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arXiv2019

Tricritical point with fractional supersymmetry from a Fibonacci topological state

We consider a generic Fibonacci topological wave function on a square lattice, and the norm of this wave function can be mapped into the partition function of two-coupled $ϕ^{2}$-state Potts models with $ϕ=(\sqrt{5}+1)/2$ as the golden ratio. A global phase diagram is thus established to display non-abelian topological phase transitions. The Fibonacci topological phase corresponds to an emergent new phase of the two-coupled Potts models, and continuously change into two non-topological phases separately, which are dual each other and divided by a first-order phase transition line. Under the self-duality, the Fibonacci topological state enters into the first-order transition state at a quantum tricritical point, where two continuous quantum phase transitions bifurcate. All the topological phase transitions are driven by condensation of anyonic bosons consisting of Fibonacci anyon and its conjugate. However, a fractional supersymmetry is displayed at the quantum tricritical point, characterized by a coset conformal field theory.

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arXiv2019

Gapless Coulomb state emerging from a self-dual topological tensor-network state

In the tensor network representation, a deformed $Z_{2}$ topological ground state wave function is proposed and its norm can be exactly mapped to the two-dimensional solvable Ashkin-Teller (AT) model. Then the topological (toric code) phase with anyonic excitations corresponds to the partial order phase of the AT model, and possible topological phase transitions are precisely determined. With the electric-magnetic self-duality, a novel gapless Coulomb state with quasi-long-range order is obtained via a quantum Kosterlitz-Thouless phase transition. The corresponding ground state is a condensate of pairs of logarithmically confined electric charges and magnetic fluxes, and the scaling behavior of various anyon correlations can be exactly derived, revealing the effective interaction between anyons and their condensation. Deformations away from the self-duality drive the Coulomb state into either the gapped Higgs phase or confining phase.

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arXiv2018

Spin-valley antiferromagnetism and topological superconductivity in the trilayer graphene Moire super-lattice

Exotic correlated insulating phases emerge in the ABC-stacked trilayer graphene-boron nitride Moire super-lattice at both quarter and half-filling. A single-band minimal model with valley contrasting staggered-flux is proposed to capture the relevant band structure, where the conspiracy of perfect Fermi-surface nesting and van Hove singularity strongly enhance the valley fluctuation, leading to inter-valley spiral (IVS) order at half filling. In this paper, we consider a strong coupling U(1)$_{v}\times $SU(2)$_{s}$ symmetric spin-valley model to obtain the correlated insulating state and the pairing instability near quarter filling. A significant ingredient in the strong coupling model is the Dzyaloshinsky-Moriya like interaction inherited from the flux, which breaks not only the valley SU(2)$_{v}$ symmetry but also the sub-valley spatial reflection symmetry. We discuss all the possible long-range orders stabilized by the effective spin-valley-exchange interactions, and it turns out that the flux remarkably enhance the ferro-spin inter-valley 120$^{\circ}$ order, which shares the same valley feature as the IVS order. Upon doping, the leading pairing instability lies in the inter-valley channel with a trigonally warped $p\pm ip$-wave form factor in the presence of the sub-valley reflection symmetry breaking. Depending on the sign of Hund's coupling, the total pairing state could be either spin singlet or triplet. While the spin singlet chiral topological pairing state $(p\pm ip)_{\uparrow\downarrow }-(p\pm ip)_{\downarrow \uparrow }$ is necessarily chiral, the spin triplet topological pairing state could be chiral $(p\pm ip)_{\uparrow\uparrow }+(p\pm ip)_{\downarrow \downarrow }$, or helical $(p\pm ip)_{\uparrow \uparrow }+(p\mp ip)_{\downarrow \downarrow }$.

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arXiv2018

Tensor network state approach to quantum topological phase transitions and their criticalities of $\mathbb{Z}_2$ topologically ordered states

We construct a general wave function with the topological order by introducing the $\mathbb{Z}_{2}$ gauge degrees of freedom, characterizing both the toric code state and double semion state. Via calculating the correlation length defined from the one-dimensional quantum transfer operator of the wave function norm, we can map out the complete phase diagram in terms of the parameter $λ$ and identify three different quantum critical points (QCPs) at $λ=0$, $\pm 1.73$. The first one separates the toric code phase and double semion phase, while later two describe the topological phase transitions from the toric code phase or double semion phase to the symmetry breaking phase, respectively. When mapping to the exactly solved statistical models, the norm of the tensor network wave function is transformed into the partition function of the eight-vertex model. Actually such a quantum-classical mapping can not reveal the rich structures of low-energy excitations at these three QCPs. So we further demonstrate that the full eigenvalue spectra of the transfer operators with/without the flux insertions can describe the complete quantum criticalities, which are characterized by the two-dimensional compactified free boson conformal field theories (CFTs) with the compactified radii $R=\sqrt{6}$ for the QCPs at $λ=\pm\sqrt{3}$ and $R=\sqrt{8/3}$ for the QCP at $λ=0$. For the QCP at $λ=0$, there are no anyon condensation, and the emerged matrix product operator symmetries result in a rich structure of the low-energy excitations, distinct from those of both toric code and double semion phases. Finally, we discuss the possible relation between our conformal quantum criticalities and the general (2+1) spatial-time dimensional CFTs for quantum topological phase transitions.

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arXiv2018

Decoding quantum criticalities from fermionic/parafermionic topological states

Under an appropriate symmetric bulk bipartition in a one-dimensional symmetry protected topological phase with the Affleck-Kennedy-Lieb-Tasaki matrix product state wave function for the odd integer spin chains, a bulk critical entanglement spectrum can be obtained, describing the excitation spectrum of the critical point separating the topological phase from the trivial phase with the same symmetry. Such a critical point is beyond the standard Landau-Ginzburg-Wilson paradigm for symmetry breaking phase transitions. Recently, the framework of matrix product states for topological phases with Majorana fermions/parafermions has been established. Here we first generalize these fixed-point matrix product states with the zero correlation length to the more generic ground-state wave functions with a finite correlation length for the general one-dimensional interacting Majorana fermion/parafermion systems. Then we employ the previous method to decode quantum criticality from the interacting Majorana fermion/parafermion matrix product states. The obtained quantum critical spectra are described by the conformal field theories with central charge $c\leq 1$, characterizing the quantum critical theories separating the fermionic/parafermionic topological phases from the trivial phases with the same symmetry.

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arXiv2018

Inter-valley spiral order in the Mott insulating state of a heterostructure of trilayer graphene-boron nitride

Recent experiment has shown that the ABC-stacked trilayer graphene-boron nitride Moire super-lattice at half-filling is a Mott insulator. Based on symmetry analysis and effective band structure calculation, we propose a valley-contrasting chiral tight-binding model with local Coulomb interaction to describe this Moire super-lattice system. By matching the positions of van Hove points in the low-energy effective bands, the valley-contrasting staggered flux per triangle is determined around $π/2$. When the valence band is half-filled, the Fermi surfaces are found to be perfectly nested between the two valleys. Such an effect can induce an inter-valley spiral order with a gap in the charge excitations, indicating that the Mott insulating behavior observed in the trilayer graphene-boron nitride Moire super-lattice results predominantly from the inter-valley scattering.

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arXiv2018

Classifying parafermionic gapped phases using matrix product states

In the Fock representation, we construct matrix product states (MPS) for one-dimensional gapped phases for $\mathbb{Z}_{p}$ parafermions. From the analysis of irreducibility of MPS, we classify all possible gapped phases of $\mathbb{Z}_{p}$ parafermions without extra symmetry other than $\mathbb{Z}%_{p}$ charge symmetry, including topological phases, spontaneous symmetry breaking phases and a trivial phase. For all phases, we find the irreducible forms of local matrices of MPS, which span different kinds of graded algebras. The topological phases are characterized by the non-trivial simple $\mathbb{Z}_{p}$ graded algebras with the characteristic graded centers, yielding the degeneracies of the full transfer matrix spectra uniquely. But the spontaneous symmetry breaking phases correspond to the trivial semisimple $\mathbb{Z}_{p/n}$ graded algebras, which can be further reduced to the trivial simple $\mathbb{Z}_{p/n}$ graded algebras, where $n$ is the divisor of $p$. So the present results deepen our understanding of topological phases in one dimension from the viewpoints of MPS.

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arXiv2018

Enriched classification of parafermionic gapped phases with time reversal symmetry

Based on the recently established parafermionic matrix product states, we study the classification of one-dimensional gapped phases of parafermions with the time reversal (TR) symmetry satisfying $T^{2}=1$. Without extra symmetry, it has been found that $\mathbb{Z}_{p}$ parafermionic gapped phases can be classified as topological phases, spontaneous symmetry breaking (SSB) phases, and a trivial phase, which are uniquely labelled by the divisors $n$ of $p$. In the presence of TR symmetry, however, the enriched classification is characterized by three indices $n$, $κ$ and $μ$, where $κ\in \mathbb{Z}_{2}$ denotes the linear or projective TR actions on the edges, and $μ\in \mathbb{Z}_{2}$ indicates the commutation relations between the TR and (fractionalized) charge operator. For the $\mathbb{Z}_{r}$ symmetric parafermionic ground states, where $r=p$ for trivial or topological phases, and $r=p/n$ for SSB phases, the original gapped phases with odd $r$ are divided into two phases, while those phases with even $r$ are further separated into four phases. The gapped parafermionic phases with the TR symmetry include the symmetry protected topological phases, symmetry enriched topological phases, and the SSB coexisting symmetry protected topological phases. From analyzing the structures and symmetries of their reduced density matrices of those resulting topological phases, we can obtain the topological protected degeneracies of their entanglement spectra.

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arXiv2017

Plaquette-centered rotation symmetry and octet-nodal superconductivity in $\text{KFe}_{2}\text{As}_{2}$

A plaquette-centered rotation symmetry $C_{4}^{p}$ is identified to play a significant role in determining and stabilizing the Fermi-surface structure of Fe-based superconductors. Together with the $S_{4}$ symmetry previously found, we are able to sort out the tangling orbitals and solve the puzzle of pairing symmetry of superconductivity in $\text{KFe}_{2}\text{As}_{2}$ in a simple but comprehensive way. By modeling the material with a strong coupling $t-J_{1}-J_{2}$ model, we find phase transitions of pairing symmetry driven by the competition between the local spin antiferromagnetic couplings from nodal $d_{x^2-y^2}\times s_{x^2+y^2}$-wave to nodeless $% s_{x^2 y^2} $-wave through the intermediate $s+id\times s$ mixed pairing phase, which is consistent with the observation of pressure experiments. The emergent $d$-wave form factor inevitably arises from the projection of inter-orbital Cooper pairing onto the Fermi surface and is inherited from the electronic structure in the representation of $C_{4}^{p}$ symmetry. Moreover, the $S_{4}$ symmetry dictates 2 copies of $d$-wave pairing condensates, counting 8 nodes in total. We further show that weakly breaking $C_{4}^{p}$ naturally leads to the octet nodal gap as precisely observed in laser angle resolved photoemission spectroscopy. The octet nodes reflect the collaboration of the $C_{4}^{p}$ and $S_{4}$ symmetries, which sheds new light on the enigma of the pairing symmetry in $\text{KFe}_{2}\text{As}_{2}$.

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arXiv2017

Topological phase transition from nodal to nodeless d-wave superconductivity in electron-doped cuprate superconductors

Unlike the hole-doped cuprates, both nodal and nodeless superconductivity (SC) are observed in the electron-doped cuprates. To understand these two types of SC states, we propose a unified theory by considering the two-dimensional t-J model in proximity to an antiferromagnetic (AF) long-range ordering state. Within the slave-boson mean-field approximation, the d-wave pairing symmetry is still the most energetically favorable even in the presence of the external AF field. In the nodal phase, it is found that the nodes carry vorticity and are protected by the adjoint symmetry of time-reversal and one unit lattice translation. Robust edge modes are obtained, suggesting the nodal d-wave SC being a topological weak-pairing phase. As decreasing the doping concentration or increasing the AF field, the nodes with opposite vorticity annihilate and the nodeless strong-pairing phase emerges. The topological phase transition is characterized by a critical point with anisotropic Bogoliubov quasiparticles, and a universal understanding is thus established for all electron-doped cuprates.

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arXiv2017

Matrix product states for topological phases with parafermions

In the Fock representation, we propose a framework to construct the generalized matrix product states (MPS) for topological phases with $\mathbb{ Z}_{p}$ parafermions. Unlike the $\mathbb{Z}_{2}$ Majorana fermions, the $% \mathbb{Z}_{p}$ parafermions form intrinsically interacting systems. Here we explicitly construct two topologically distinct classes of irreducible $% \mathbb{Z}_{3}$ parafermionic MPS wave functions, characterized by one or two parafermionic zero modes at each end of an open chain. Their corresponding parent Hamiltonians are found as the fixed point models of the single $\mathbb{Z}_{3}$ parafermion chain and two-coupled parafermion chains with $\mathbb{Z}_{3}\times \mathbb{Z}_{3}$ symmetry. Our results thus pave the road to investigate all possible topological phases with $\mathbb{Z}_{p}$ parafermions within the matrix product representation in one dimension.

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arXiv2017

Two-dimensional topological superconducting phases emerged from d-wave superconductors in proximity to antiferromagnets

Motivated by the recent observations of nodeless superconductivity in the monolayer CuO$_{2}$ grown on the Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ substrates, we study the two-dimensional superconducting (SC) phases described by the two-dimensional $t$-$J$ model in proximity to an antiferromagnetic (AF) insulator. We found that (i) the nodal d-wave SC state can be driven via a continuous transition into a nodeless d-wave pairing state by the proximity induced AF field. (ii) The energetically favorable pairing states in the strong field regime have extended s-wave symmetry and can be nodal or nodeless. (iii) Between the pure d-wave and s-wave paired phases, there emerge two topologically distinct SC phases with ($s+$i$d$) symmetry, i.e., the weak and strong pairing phases, and the weak pairing phase is found to be a $Z_{2}$ topological superconductor protected by valley symmetry, exhibiting robust gapless non-chiral edge modes. These findings strongly suggest that the high-$T_{c}$ superconductors in proximity to antiferromagnets can realize fully gapped symmetry protected topological SC.

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