**Z2 Gauge Theory**. The ising* conﬁnement transition 3. Requires gauge ﬁxing to have an integration measure that sumsovergauge classes of conﬁgurations.

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(1) the degrees of freedom in this partition function are the binary variables ˙ ij = 1 on the links ‘ (ij) of the cubic lattice. They are aimed at beginning graduate students. We will use the notation u µ ≡ τ µ.withτ µ = ±1.

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We note that the very nature of this deconfined phase is the key underlying topological order in kitaev’s toric code [8]. Zz lattice gauge model the partition function of the zz lattice gauge theory is given by links q ;

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Since the ising gauge field mediates attraction. when coupled to fermionic matter it leads to formation of an exotic superfluid state. In the limit of strong string tension. we uncover emergent integrable correlated hopping dynamics of holes which is complementary to.

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We will use the notation u µ ≡ τ µ.withτ µ = ±1. We will jump directly to the quantized version of the theory.

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Choosing the value of hi for each vertex i amounts to choosing a gauge. Is de ned on the link labeled by a site nwith a direction.

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Is de ned on the link labeled by a site nwith a direction. Simulating z2 gauge theory and kitaevs toric code.

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2 gauge theory the partition function: 2lattice gauge theory and topological order 2.

#### The Main Idea Is To Switch From Integer Arithmetics (ℤ) To Binary One (ℤ2) For The Electric Flux Through Lattice Links.

We will specialize to d=2 here. Φstr = φstr . φstr = φstr • the hamiltonian to enforce the dancing rules: (1) the degrees of freedom in this partition function are the binary variables ˙ ij = 1 on the links ‘ (ij) of the cubic lattice.

#### We Will Jump Directly To The Quantized Version Of The Theory.

Ising gauge theory has a local z2 symmetry. tz ij!hi t z ij hj (3) where hi = i1 can be chosen arbitrarily at each site in the dual lattice. Such gauge theories in higher dimensions are interesting in condensed matter physics and are believed to describe frustrated quantum magnets and spin liquid phases of materials [19] . [20] and have also been studied by. Transition of z2 gauge theory in four dimensions.

#### _ 1 W Where The Link Variable A .. Is Labeled By The Link Leaving The Lattice Point N = (R. X) In .U = 0.1. 2. 3 Direction.

We consider the partition function [1] ze z 2 = x f˙ ijg= 1 exp he z 2 =t he z 2 = k x (y ij)2 ˙ ij; Is de ned on the link labeled by a site nwith a direction. Simulating z2 gauge theory and kitaevs toric code.

#### Examples Of Gauge Theories Are. Z 2:Thisistheisinggaugetheory.Whosegaugegroupisz 2.(Wegner.1971;

We will use the notation u µ ≡ τ µ.withτ µ = ±1. In the language of the lattice gauge theory. one of the couplings controls the “stiffness” In a collaboration with the experimental group of monika aidelsburger and immanuel bloch (lmu) the elementary building block for z2 lattice gauge theories coupled to matter was realized.

#### N T Corresponds The Temperature.

Theoretical discovery of the ising z2 gauge theory led to a drastic shift of paradigm of our understanding of phase transitions and was the first example of a system that exhibits topological order. In the quantum language. these two couplings allow us to separately control the masses of both e and m excitations. Zz lattice gauge model the partition function of the zz lattice gauge theory is given by links q ;