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 lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation

Homeier, Lukas; Schweizer, C.; Aidelsburger, Monika; Fedorov, Arkady; Grusdt, Fabian

doi:10.1103/physrevb.104.085138

Cited by 28 publications

(4 citation statements)

References 74 publications

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“…Moreover it would be desirable to compare our results to experiments. In particular the Rydberg dressing scheme where the model maps exactly to a t − J z model [27] is a promising approach which could be implemented in a cold atom experiment in addition to the already mentioned Floquet scheme [8][9][10], superconducting qubits [11,12] and recent Rydberg tweezer array proposals [14,15] [30]. Such mapping gives us the XXZ model up to constant factors [30]…”

Section: Discussionmentioning

confidence: 99%

“…Significant progress has also been made in simulating Z 2 LGT models by using Floquet schemes [8], with experimentally realized building blocks which have potential to be scaled to bigger system sizes [9,10]. Furthermore, it has also been shown that the Z 2 LGTs could be implemented using superconducting qubits [11,12]. More recently, a Rydberg tweezer array implementation [13] which utilizes the so called local-pseudo-generators [14,15] has been proposed.…”

Section: Introductionmentioning

confidence: 99%

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Confinement induced frustration in a one-dimensional Z2 lattice gauge theory

et al. 2023

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Coupling dynamical charges to gauge fields can result in highly non-local interactions with a linear confining potential. As a consequence, individual particles bind into mesons which, in one dimension, become the new constituents of emergent Luttinger liquids (LLs). Furthermore, at commensurate fillings, different Mott-insulating states can be stabilized by including nearest-neighbour (NN) interactions among charges. However, rich phase diagrams expected in such models have not been fully explored and still lack comprehensive theoretical explanation. Here, by combining numerical and analytical tools, we study a simple one-dimensional Z 2 lattice gauge theory at half-filling, where U(1) matter is coupled to gauge fields and interacts through NN repulsion. We uncover a rich phase diagram where the local NN interaction stabilizes a Mott state of individual charges (or partons) on the one hand, and an LL of confined mesons on the other. Furthermore, at the interface between these two phases, we uncover a highly frustrated regime arising due to the competition between the local NN repulsion and the non-local confining interactions, realizing a pre-formed parton plasma. Our work is motivated by the recent progress in ultracold atom experiments, where such simple model could be readily implemented. For this reason we calculate the static structure factor which we propose as a simple probe to explore the phase diagram in an experimental setup.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Confinement induced frustration in a one-dimensional Z2 lattice gauge theory

et al. 2023

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“…The proposed protocol can also be applied in a larger range of systems whenever effective interactions are induced through virtual higher-order processes. Examples include U(1) lattice gauge theories in Bose-Hubbard systems [8], ring-exchange interactions [37], and Z 2 lattice gauge theories with superconducting qubits [38].…”

Section: Discussionmentioning

confidence: 99%

Schrieffer-Wolff transformations for experiments: Dynamically suppressing virtual doublon-hole excitations in a Fermi-Hubbard simulator

Kale

Huhn²,

et al. 2022

Phys. Rev. A

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In strongly interacting systems with a separation of energy scales, low-energy effective Hamiltonians help provide insights into the relevant physics at low temperatures. The emergent interactions in the effective model are mediated by virtual excitations of high-energy states: For example, virtual doublon-hole excitations in the Fermi-Hubbard model mediate antiferromagnetic spin-exchange interactions in the derived effective model, known as the t − J − 3s model. Formally this procedure is described by performing a unitary Schrieffer-Wolff basis transformation. In the context of quantum simulation, it can be advantageous to consider the effective model to interpret experimental results. However, virtual excitations such as doublon-hole pairs can obfuscate the measurement of physical observables. Here we show that quantum simulators allow one to access the effective model even more directly by performing measurements in a rotated basis. We propose a protocol to perform a Schrieffer-Wolff transformation on Fermi-Hubbard low-energy eigenstates (or thermal states) to dynamically prepare approximate t − J − 3s model states using fermionic atoms in an optical lattice. Our protocol involves performing a linear ramp of the optical lattice depth, which is slow enough to eliminate the virtual doublon-hole fluctuations but fast enough to freeze out the dynamics in the effective model. We perform a numerical study using exact diagonalization and find an optimal ramp speed for which the state after the lattice ramp has maximal overlap with the t − J − 3s model state. We compare our numerics to experimental data from our Lithium-6 fermionic quantum gas microscope and show a proof-of-principle demonstration of this protocol. More generally, this protocol can be beneficial to studies of effective models by enabling the suppression of virtual excitations in a wide range of quantum simulation experiments.

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“…Recently, DQPTs have also been studied in gauge theories [46,47], a class of quantum many-body models describing the interactions between dynamical matter and gauge fields through local constraints enforced by the underlying gauge symmetries [48][49][50]. Lattice gauge theories (LGTs) have recently been at the center of a number of impressive quantum-simulation experiments [51][52][53][54][55][56][57][58][59][60][61], and there is great interest in advancing these setups to quantum simulate more complex gauge theories [62][63][64][65][66][67][68]. Though initially a tool to address nonperturbative regimes in high-energy physics [49],…”

Section: Introductionmentioning

confidence: 99%

Dynamical quantum phase transitions in spin- S U(1) quantum link models

et al. 2022

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Dynamical quantum phase transitions (DQPTs) are a powerful concept of probing far-from-equilibrium criticality in quantum many-body systems. With the strong ongoing experimental drive to quantum simulate lattice gauge theories, it becomes important to investigate DQPTs in these models in order to better understand their far-from-equilibrium properties. In this work, we use infinite matrix product state techniques to study DQPTs in spin-S U (1) quantum link models. Although we are able to reproduce literature results directly connecting DQPTs to a sign change in the dynamical order parameter in the case of S = 1/2 for quenches starting in a vacuum initial state, we find that for different quench protocols or different values of the link spin length S > 1/2 this direct connection is no longer present. In particular, we find that there is an abundance of different types of DQPTs not directly associated with any sign change of the order parameter. Our findings indicate that DQPTs are fundamentally different between the Wilson-Kogut-Susskind limit and its representation through the quantum link formalism.

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Z2 lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation

Cited by 28 publications

References 74 publications

Confinement induced frustration in a one-dimensional Z2 lattice gauge theory

Confinement induced frustration in a one-dimensional Z2 lattice gauge theory

Schrieffer-Wolff transformations for experiments: Dynamically suppressing virtual doublon-hole excitations in a Fermi-Hubbard simulator

Dynamical quantum phase transitions in spin- S U(1) quantum link models

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