Recently, we presented a systematic recipe for generating duality transformations in one dimensional lattice models. Our construction is based on a detailed understanding of the most general kind of symmetry a one-dimensional lattice model can exhibit: categorical symmetries. These symmetries are conveniently described in the language of tensor networks, where they are represented as matrix product operators. For a given lattice model with such categorical symmetries, their mathematical description in terms of bimodule categories allows us to generate all possible dual models, as well as explicit matrix product operator intertwiners that implement the dualities at the level of the Hilbert space.
In this talk, I will provide an overview of these results by giving an introduction to matrix product operator symmetries, the underlying categorical structures and how they provide the right framework for studying dualities. I will discuss some well known examples to illustrate our framework, and show how the categorical approach allows us to precisely relate the various symmetry sectors of dual models to each other.
Based on arXiv:2008.11187 and arXiv:2112.09091
Join Zoom Meeting
https://umd.zoom.us/j/9893676372?pwd=VVNOd2xNZ3FCblk4aFdTMjkzTllvQT09
Meeting ID: 989 367 6372
Passcode: abc123
One tap mobile
+16699006833,,9893676372# US (San Jose)
+19294362866,,9893676372# US (New York)
Dial by your location
+1 669 900 6833 US (San Jose)
+1 929 436 2866 US (New York)
+1 253 215 8782 US (Tacoma)
+1 301 715 8592 US (Washington DC)
+1 312 626 6799 US (Chicago)
+1 346 248 7799 US (Houston)
+1 386 347 5053 US
+1 564 217 2000 US
+1 646 931 3860 US
+1 669 444 9171 US
Meeting ID: 989 367 6372
Find your local number: https://umd.zoom.us/u/abF3cNNZ0B
Join by SIP
9893676372@zoomcrc.com
Join by H.323
162.255.37.11 (US West)
162.255.36.11 (US East)
115.114.131.7 (India Mumbai)
115.114.115.7 (India Hyderabad)
213.19.144.110 (Amsterdam Netherlands)
213.244.140.110 (Germany)
103.122.166.55 (Australia Sydney)
103.122.167.55 (Australia Melbourne)
149.137.40.110 (Singapore)
64.211.144.160 (Brazil)
149.137.68.253 (Mexico)
69.174.57.160 (Canada Toronto)
65.39.152.160 (Canada Vancouver)
207.226.132.110 (Japan Tokyo)
149.137.24.110 (Japan Osaka)
Meeting ID: 989 367 6372
Passcode: 578842