Relating entanglement spectra and energy spectra via path-integral on replica manifold

Zheng, Yufeng; Meng, Zi Yang

doi:10.48550/arxiv.2112.05886

Cited by 3 publications

(3 citation statements)

References 61 publications

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“…, where 𝑛 0 is the particle density, which is 1/2 at low-temperature and 𝑁 = k 1 ,𝑚 1 𝑑 † k 1 ,𝑚 1 𝑑 k 1 ,𝑚 1 is the particle number operator. We also compute the temperature dependence of the spetral functions from the stochastic analytic continuation (SAC) of the imaginary time Green's function from QMC [36,51,[61][62][63] and perform the finite size scaling of the order parameter for the QAH phase and find a good agreement with Ising universality. The topological aspect of the QAH phase can be also seen from the computed Berry curvature below the transition temperature, and from which the Chern numbe can then be calculated as 𝐶 = 𝐹 , where 𝐹 is the Berry curvature in the finite size mBZ obtained from the Green's function in the QMC simulations [64,65].…”

mentioning

confidence: 88%

Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state

Pan¹,

Lu²,

Li³

et al. 2022

Preprint

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While the ground state phase diagram of the correlated flat-band systems have been intensively investigated, the dynamic and thermodynamic properties of such lattice models are less explored, but it is the latter which is most relevant to the experimental probes (transport, quantum capacitance and spectroscopy) of the quantum moiré materials such as twisted bilayer graphene and transition metal dichalcogenides. Here we show, by means of momentum-space quantum Monte Carlo and exact diagonalization, there exists a unique thermodynamic characteristic for the correlated flat-band models with interaction-driven quantum anomalous Hall (QAH) ground state, namely, the transition from the QAH insulator to the metallic state takes place at a much lower temperature compared with the zero-temperature single-particle gap generated by the long-range Coulomb interaction. Such low transition temperature comes from the proliferation of excitonic particle-hole excitations, which "quantum teleport" the electrons across the gap between different topological bands to restore the broken time-reversal symmetry and give rise to a pronounced enhancement in the charge compressibility. Future experiments, to verify such generic thermodynamic characteristics, are proposed.

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confidence: 88%

Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state

Pan¹,

Lu²,

Li³

et al. 2022

Preprint

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“…We note a similar geometry has been used in the computation of entanglement spectrum in (2+1)d quantum many-body systems [58]. The disorder parameter is then given by…”

Section: Acknowledgementmentioning

confidence: 99%

Topological Disorder Parameter

Chen,

Tu,

Meng

et al. 2022

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We introduce a many-body topological invariant, called the topological disorder parameter (TDP), to characterize gapped quantum phases with global internal symmetry in (2+1)d. TDP is defined as the constant correction that appears in the ground state expectation value of a partial symmetry transformation applied to a connected spatial region M , the absolute value of which scales generically as exp(−αl+γ) where l is the perimeter of M and γ is the TDP. Motivated by a topological quantum field theory interpretation of the operator, we show that e γ can be related to the quantum dimension of the symmetry defect, and provide a general formula for γ when the entanglement Hamiltonian of the topological phase can be described by a (1+1)d conformal field theory (CFT). A special case of TDP is equivalent to the topological Rényi entanglement entropy when the symmetry is the cyclic permutation of the replica of the gapped phase. We then investigate several examples of lattice models of topological phases, both analytically and numerically, in particular when the assumption of having a CFT edge theory is not satisfied. We also consider an example of partial translation symmetry in Wen's plaquette model and show that the result can be understood using the edge CFT. Our results establish a new tool to detect quantum topological order.

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“…Such topological unit provides a stable and efficient way of carrying out the computation both conceptually and technically. Beyond the 2-leg geometry, a general n-leg Qiu Ku manifold can even give rise to the low-lying entanglement spectrum for quantum manybody systems [33].…”

Section: Introductionmentioning

confidence: 99%

Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations

Zhao,

Chen,

Wang

et al. 2021

Preprint

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To hear the shape of a quantum drum is in principle not a mission impossible, where the shape means the conformal field theory (CFT) description of certain quantum phases and phase transitions in a (2 + 1)d manifold and the drum beat means some characteristic (such as spectral) measurements of the quantum system whose structure reveals the CFT information. In realistic quantum many-body lattice models, however, measurements such as the finite size scaling of the entanglement entropy with reliable data to extract the CFT characteristics, are rare due to the numerical difficulties in the precise measurement of entanglement with replicas of the partition functions. To overcome this problem, we design a generic computation protocol to obtain the Rényi entanglement entropy of the aforementioned systems with efficiency and precision. Our method, dubbed "Qiu Ku" algorithm, is based on the massive parallelization of the nonequilibrium increment processes in quantum Monte Carlo simulations. To demonstrate its power, we show the results on a few important yet difficult (2 + 1)d quantum lattice models, ranging from Heisenberg quantum antiferromagnet with spontaneous symmetry breaking, quantum critical point with O(3) CFT to the toric code Z2 topological ordered state and the Kagome Z2 quantum spin liquid model with frustration and multi-spin interactions. In all these cases, our method reveals either the precise CFT data from the logarithmic correction or quantum dimension of the topological order, with unprecedentedly large system sizes, controlled errorbars and minimal computational costs. Our "Qiu Ku" algorithm therefore helps one to clearly hear the shapes of various difficult yet important quantum drums.

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Relating entanglement spectra and energy spectra via path-integral on replica manifold

Cited by 3 publications

References 61 publications

Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state

Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state

Topological Disorder Parameter

Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations

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