Tensor network simulation of the (
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)-dimensional 
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 nonlinear 
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Wei, Tang; Xie, X. C.; Wang, Lei; Tu, Hong-Hao

doi:10.1103/physrevd.104.114513

Cited by 5 publications

(5 citation statements)

References 47 publications

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“…This makes it possible to construct the Kac-Moody generator for systems where the Hamiltonian is not available. One example is the cMPS in the continuous matrix product operator simulation [47,48], where the cMPS is the dominant eigenvector of the quantum transfer matrix. Another possible research direction is to consider possible extensions of the cMPS ansatz with a fixed particle number.…”

Section: Discussionmentioning

confidence: 99%

“…In addition to ground-state simulations, cMPS can also be used to compute excited states [41] and time evolution [42,43]. In addition, cMPS can be related to continuous measurements [44], open quantum systems [45], classical stochastic dynamics [46], and thermodynamics of quantum lattice systems [47,48]. Moreover, there also exist generalizations of the cMPS ansatz, such as the relativistic cMPS [49], and the continuous projected entangled-pair states [50,51].…”

Section: Kac-moody Generators In Continuous Matrix Product Statesmentioning

confidence: 99%

“…Before we proceed to compute the overlaps in Eqs. (48), we first introduce the following notations. Suppose the cMPS transfer matrix T has the eigendecomposition T = U U −1 .…”

Section: Computation Of the Effective Hamiltonian And The Effective N...mentioning

confidence: 99%

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Kac-Moody symmetries in one-dimensional bosonic systems

Tang,

Haegeman

2023

Phys. Rev. B

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In conformal field theories, when the conformal symmetry is enhanced by a global Lie group symmetry, the original Virasoro algebra can be extended to Kac-Moody algebra. In this paper, we extend the lattice construction of the Kac-Moody generators introduced in Wang et al., [Phys. Rev. B 106, 115111 (2022)] to continuous systems and apply it to one-dimensional continuous boson systems. We justify this microscopic construction of Kac-Moody generators in two ways. First, through phenomenological bosonization, we express the microscopic construction in terms of the boson operators in the bosonization context, which can be related to the Kac-Moody generators in conformal field theories. Second, we study the behavior of the Kac-Moody generators in the integrable Lieb-Liniger model and reveal its underlying particle-hole excitation picture through Bethe ansatz solutions. Finally, we test the computation of the Kac-Moody generator in the continuous matrix product state simulations, paving the way for more challenging nonintegrable systems.

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Section: Discussionmentioning

confidence: 99%

Section: Kac-moody Generators In Continuous Matrix Product Statesmentioning

confidence: 99%

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Kac-Moody symmetries in one-dimensional bosonic systems

Tang,

Haegeman

2023

Phys. Rev. B

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“…For a small number of lattice sites and modest truncation, we can compute the energy gap and ground state energy using the exact diagonalization (ED) method. The state-of-the-art classical method is tensor networks and this model has been studied using matrix product states (MPS) with and without the topological 𝜃-term [11,12] We show the ED results in Fig. 1 and Fig.…”

Section: Exact Diagonalization and Beyondmentioning

confidence: 99%

Quantum computations of the 𝑶(3) model using qumodes

Jha,

Ringer,

Siopsis

et al. 2024

Proceedings of the 40th International Symposium on Lattice Field Theory — PoS(LATTICE2023)

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We express the discrete 1+1-dimensional 𝑂 (3) non-linear sigma model (NL𝜎M) in a form wellsuited for the continuous variable approach to quantum computing. Within the Schwinger boson formulation, we need two qumodes (quantum-mechanical oscillators) at each lattice site. We envision that it might be possible to reach the scaling regime of this model and observe asymptotic freedom on near-term photonic quantum devices in the coming decade.

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“…The entanglement entropy for the general cMPS can be calculated by Schmidt decomposition. [28] For the Ising cMPS in Eq. (E6), the corresponding normalized state is…”

Section: C5 Derive Integral Equationmentioning

confidence: 99%

Structure of continuous matrix product operator for transverse field Ising model: An analytic and numerical study

Zhang

Wang

2022

Chinese Phys. B

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We study the structure of the continuous matrix product operator (cMPO) [1] for the transverse field Ising model (TFIM). We prove TFIM's cMPO is solvable and has the form $T=e^{-\frac{1}{2}\hat{H}_F}$. $\hat{H}_F$ is a non-local free fermionic hamiltonian on a ring with circumference $\beta$, whose ground state is gapped and non-degenerate even at the critical point. The full spectrum of $\hat{H}_F$ is determined analytically. At the critical point, our results verify the state-operator-correspondence [2] in the conformal field theory (CFT). We also design a numerical algorithm based on Bloch state ansatz to calculate the low-lying excited states of general (hermitian) cMPO. Our numerical calculations coincide with the analytic results of TFIM. In the end, we give a short discussion about the entanglement entropy of cMPO's ground state.

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Tensor network simulation of the ( 1+1 )-dimensional O(3) nonlinear σ

Cited by 5 publications

References 47 publications

Kac-Moody symmetries in one-dimensional bosonic systems

Kac-Moody symmetries in one-dimensional bosonic systems

Quantum computations of the 𝑶(3) model using qumodes

Structure of continuous matrix product operator for transverse field Ising model: An analytic and numerical study

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