Topological and symmetry-enriched random quantum critical points

Duque, Carlos M.; Hu, Hong-Ye; You, Yi-Zhuang; Khemani, Vedika; Verresen, Ruben; Vasseur, Romain

doi:10.1103/physrevb.103.l100207

Cited by 25 publications

(11 citation statements)

References 98 publications

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“…One should be able to perform such a study also directly in the spin variables using the SBRG approach of [4] projected onto the ground state branch, e.g., as used in Ref. [66] in a different problem. Employing the insights gained here, it should be helpful to interpret various Pauli string terms generated under the SBRG as either Majorana hoppings or specific multifermion interactions.…”

Section: Discussionmentioning

confidence: 99%

Infinite randomness with continuously varying critical exponents in the random XYZ spin chain

Roberts

Motrunich

2021

Phys. Rev. B

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We study the antiferromagnetic XYZ spin chain with quenched bond randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation using the spectrum-bifurcation renormalization group, and assuming marginal many-body localization, proposed that critical indices vary continuously. In this work, we solve the low-energy physics using an unbiased numerically exact tensor network method named the "rigorous renormalization group." We find a line of fixed points consistent with infinite-randomness phenomenology, with indeed continuously varying critical exponents for average spin correlations. A self-consistent Hartree-Fock-type treatment of the z couplings as interactions added to the free-fermion random XY model captures much of the important physics including the varying exponents; we provide an understanding of this as a result of local correlation induced between the mean-field couplings. We solve the problem of the locally correlated XY spin chain with an arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on an associated classical random walk problem. This is also an example of a line of fixed points with continuously varying exponents in the equivalent disordered free-fermion chain. We argue that this line of fixed points also controls an extended region of the critical interacting XYZ spin chain.

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Section: Discussionmentioning

confidence: 99%

Infinite randomness with continuously varying critical exponents in the random XYZ spin chain

Roberts

Motrunich

2021

Phys. Rev. B

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“…One should be able to perform such a study also directly in the spin variables using the SBRG approach of Slagle et al [4] projected onto the ground state branch, e.g., as used in Ref. [67] in a different problem. Employing the insights gained here, it should be helpful to interpret various Pauli string terms generated under the SBRG as either Majorana hoppings or specific multi-fermion interactions.…”

Section: Discussionmentioning

confidence: 99%

Infinite randomness with continuously varying critical exponents in the random XYZ spin chain

Roberts,

Motrunich

2021

Preprint

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We study the antiferromagnetic XYZ spin chain with quenched randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation of Slagle et al., Phys. Rev. B 94, 014205 (2016), using the spectrum-bifurcation renormalization group and assuming marginal many-body localization, proposed that critical indices for Edwards-Anderson correlators vary continuously. In this work we solve the low-energy physics using an unbiased numerically exact tensor network method named the "rigorous renormalization group." We find a line of fixed points consistent with infinite-randomness phenomenology, with critical exponents for average spin correlations varying continuously. The phase boundary tunes from a free-fermion fixed point to an S3-symmetric multicritical point. For weak microscopic interactions, a self-consistent Hartree-Fock-type treatment captures much of the important physics including the varying exponents; we provide an understanding of this as a result of local correlation induced between the mean-field couplings. We then solve the problem of the locally-correlated XY spin chain with arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on the survival probability of an associated classical random walk problem. This is also an example of a line of fixed points with continuously varying exponents in the equivalent disordered free-fermion chain. Finally, we conjecture that this line of fixed points also controls the critical XYZ spin chain for small interaction strength.

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“…However, applying this Jordan-Wigner transformation to H XXZ will lead to four-fermion interactions for ∆ = 0. We also note that a model with these interaction terms appears in the literature as a 'twisted' XXZ chain [11,40,41]. However, that model is not translation invariant and moreover contains additional interactions, meaning that it is not equivalent to H XXZ .…”

Section: A Locality-preserving Transformations With K = 2 and The Xxz...mentioning

confidence: 96%

Integrable spin chains and the Clifford group

Jones¹,

Linden²

2021

Preprint

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We construct new families of spin chain Hamiltonians that are local, integrable and translationally invariant. To do so, we make use of the Clifford group that arises in quantum information theory. We consider translation invariant Clifford group transformations that can be described by matrix product operators (MPOs). We classify the translation invariant Clifford group transformations that consist of a shift operator and an MPO of bond dimension two-this includes transformations that preserve locality of all Hamiltonians; as well as those that lead to non-local images of particular operators but nevertheless preserve locality of certain Hamiltonians. We characterise the translation invariant Clifford group transformations that take single-site Pauli operators to local operators on at most five sites-examples of Quantum Cellular Automata-leading to a discrete family of Hamiltonians that are equivalent to the canonical XXZ model under such transformations. For spin chains solvable by algebraic Bethe Ansatz, we explain how conjugating by a matrix product operator affects the underlying integrable structure. This allows us to relate our results to the usual classifications of integrable Hamiltonians. We also treat the case of spin chains solvable by free fermions.

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Topological and symmetry-enriched random quantum critical points

Cited by 25 publications

References 98 publications

Infinite randomness with continuously varying critical exponents in the random XYZ spin chain

Infinite randomness with continuously varying critical exponents in the random XYZ spin chain

Infinite randomness with continuously varying critical exponents in the random XYZ spin chain

Integrable spin chains and the Clifford group

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