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We demonstrate that supervised machine learning (ML) with entanglement spectrum can give useful information for constructing phase diagram in the half-filled one-dimensional extended Hubbard model.
K. Shinjo, S. Sota, S. Yunoki, T. Tohyama, arXiv:1901.07900
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We take the following parameter spaces as training dataset: { 5 < U < 7 , 1 < V < 2 } \{5<U<7,1<V<2\} , { 1 < U < 7 , V = U / 2 − 0.3 } \{1<U<7,V=U/2-0.3\} , { 3 < U < 4 , − 1.5 < V < − 1.0 } \{3<U<4,-1.5<V<-1.0\} , and { 4 < U < 10 , − 1 < V < 0 } \{4<U<10,-1<V<0\} for MI phase, { 4.5 < U < 5.5 , 4 < V < 5 } \{4.5<U<5.5,4<V<5\} , { − 10 < U < − 5 , 0.1 < V < 1.1 } \{-10<U<-5,0.1<V<1.1\} , { − 6 < U < − 1 , 0.01 < V < 1.01 } \{-6<U<-1,0.01<V<1.01\} , and { − 1 < U < 0 , 4 < V < 5 } \{-1<U<0,4<V<5\} for CDW phase, { 0.5 < U < 1 , V = U / 2 } \{0.5<U<1,V=U/2\} and { 3.5 < U < 4.5 , V = U / 2 } \{3.5<U<4.5,V=U/2\} for BOW phase, { − 3 < U < − 4 , − 0.3 < V < − 0.2 } \{-3<U<-4,-0.3<V<-0.2\} and { − 9 < U < − 8 , − 0.1 < V < − 0.2 } \{-9<U<-8,-0.1<V<-0.2\} for singlet-SC phase, { − 2.5 < U < − 2.0 , − 1 < V < − 0.8 } \{-2.5<U<-2.0,-1<V<-0.8\} , { 0.5 < U < 0.8 , − 0.9 < V < − 0.8 } \{0.5<U<0.8,-0.9<V<-0.8\} , and { 0.2 < U < 0.5 , − 0.7 < V < − 0.5 } \{0.2<U<0.5,-0.7<V<-0.5\} for triplet-SC phase, and { 0 < U < 1 , − 4 < V < − 5 } \{0<U<1,-4<V<-5\} and { − 4 < U < − 3 , − 5 < V < − 2 } \{-4<U<-3,-5<V<-2\} for PS phase
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