Competing topological orders in three dimensions

Mühlhauser, M.; Schmidt, K. P.; Vidal, Julien; Walther, M. R.

doi:10.21468/scipostphys.12.2.069

Cited by 13 publications

(9 citation statements)

References 60 publications

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“…This view also holds near the TC phase if one interpret the electric string turning point as a monopole, and the resonant state of an electric charge octupole around an elementary cube satisfying ∏ l∈ σ x l = −1 as a fracton. Viewed in the basis of the topological defects, such tuning parameter couples to the onsite diagonal mass for a given single topological defect, which explains the first order transition found by the authors [38]. In contrast, the gauge fluctuations are interactions between topological defects at different locations, such as the pair annihilation of the monopoles from adjacent vertices, or the loop fluctuation of the magnetic flux penetrating different faces.…”

Section: Comparison With Previous Studies Into the Fracton Qptmentioning

confidence: 91%

“…[36] to pin the location of transition point. In a more recent paper the authors also use the same series expansion method to study a phase diagram of directly interpolating the Hamiltonian between the 3D toric code and X cube model [38], by tuning the coupling constant of the XC inplane star and cube stabilizer terms from a TC phase. Although their phase diagram also consists of both 3D TC and XC phases, bearing certain similarity to our phase diagram, the nature of their phase transitions are qualitatively sharply distinct from ours: by directly tuning the inplane star stabilizer terms Â+ , the authors therein are essentially tuning the rest mass of a monopole in XC phase; likewise, tuning the cube stabilizer terms ∏ l∈ σ x l is equivalent to tuning the rest mass of a fracton defect.…”

Section: Comparison With Previous Studies Into the Fracton Qptmentioning

confidence: 99%

“…One is the principal nature of quantum phase transitions (QPTs) involving fracton topological phases, which due to their non-local structure have to go beyond the traditional Landau-Ginzburg-Wilson paradigm. Although there have been analytical attempts based on Hamiltonian duality, series expansions or phenomenological field theories [13,[33][34][35][36][37][38], a direct microscopic investigation, e.g., by considering deformations of exactly solvable Hamiltonians as for their 2D counterparts, has remained largely out of scope of current approaches.…”

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confidence: 99%

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Topological fracton quantum phase transitions by tuning exact tensor network states

Zhu¹,

Chen²,

Ye³

2022

Preprint

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Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable models remains a formidable challenge. Here we employ an exact 3D quantum tensor-network approach that allows us to study a Z N generalization of the prototypical X cube fracton model and its quantum phase transitions between distinct topological states via fully tractable wavefunction deformations. We map the (deformed) quantum states exactly to a combination of a classical lattice gauge theory and a plaquette clock model, and employ numerical techniques to calculate various entanglement order parameters.For the Z N model we find a family of (weakly) first-order fracton confinement transitions that in the limit of N → ∞ converge to a continuous phase transition beyond the Landau-Ginzburg-Wilson paradigm. We also discover a line of 3D conformal quantum critical points (with critical magnetic flux loop fluctuations) which, in the N → ∞ limit, appears to coexist with a gapless deconfined fracton state.

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Section: Comparison With Previous Studies Into the Fracton Qptmentioning

confidence: 91%

Section: Comparison With Previous Studies Into the Fracton Qptmentioning

confidence: 99%

mentioning

confidence: 99%

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Topological fracton quantum phase transitions by tuning exact tensor network states

Zhu¹,

Chen²,

Ye³

2022

Preprint

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“…An important approach for understanding fracton phases such as the X-cube model is to study quantum phase transitions out of such phases [37,38]. An important issue is to consider different indicators which can characterize a fracton phase transition.…”

Section: Introductionmentioning

confidence: 99%

Foliated order parameter in a fracton phase transition

Zarei,

Nobakht

2022

Preprint

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Finding suitable indicators for characterizing quantum phase transitions plays an important role in understanding different phases of matter. It is especially important for fracton phases where a combination of topology and fractionalization leads to exotic features not seen in other known quantum phases. In this paper, we consider the above problem by studying phase transition in the X-cube model in the presence of a non-linear perturbation. Using an analysis of the ground state fidelity and identifying a discontinuity in the global entanglement, we show there is a firstorder quantum phase transition from a type I fracton phase with a highly entangled nature to a magnetized phase. Accordingly, we conclude that the global entanglement, as a measure of the total quantum correlations in the ground state, can well capture certain features of fracton phase transitions. Then, we introduce a non-local order parameter in the form of a foliated operator which can characterize the above phase transition. We particularly show that such an order parameter has a geometric nature which captures specific differences of fracton phases with topological phases. Our study is specifically based on a well-known dual mapping to the classical plaquette Ising model where it shows the importance of such dualities in studying different quantum phases of matter.

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“…3 Projective cluster-additive transformation 12 3.1 Cluster-additivity for single particle states 12 3.2 Cluster-additivity for multi-particle excitations 13 3.3 Explicit form of transformation in terms of projection operators 15 1 Introduction…”

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confidence: 99%

Projective cluster-additive transformation for quantum lattice models

Hörmann¹,

Schmidt²

2023

Preprint

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We construct a projection-based cluster-additive transformation that block-diagonalizes wide classes of lattice Hamiltonians H = H 0 + V . Its cluster additivity is an essential ingredient to set up perturbative or non-perturbative linked-cluster expansions for degenerate excitation subspaces of H 0 . Our transformation generalizes the minimal transformation known amongst others under the names Takahashi's transformation, Schrieffer-Wolff transformation, des Cloiseaux effective Hamiltonian, canonical van Vleck effective Hamiltonian or two-block orthogonalization method. The effective cluster-additive Hamiltonian and the transformation for a given subspace of H, that is adiabatically connected to the eigenspace of H 0 with eigenvalue e n 0 , solely depends on the eigenspaces of H connected to e m 0 with e m 0 ≤ e n 0 . In contrast, other cluster-additive transformations like the multi-block orthognalization method or perturbative continuous unitary transformations need a larger basis. This can be exploited to implement the transformation efficiently both perturbatively and non-perturbatively. As a benchmark, we perform perturbative and non-perturbative linked-cluster expansions in the low-field ordered phase of the transverse-field Ising model on the square lattice for single spin-flips and two spin-flip bound-states.

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Competing topological orders in three dimensions

Cited by 13 publications

References 60 publications

Topological fracton quantum phase transitions by tuning exact tensor network states

Topological fracton quantum phase transitions by tuning exact tensor network states

Foliated order parameter in a fracton phase transition

Projective cluster-additive transformation for quantum lattice models

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