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XNNA<)96%Dma&oi5Qc#F1O2GaHDq`dk diff --git a/k-local-review.tex b/k-local-review.tex index 0c6baa1..64c378a 100644 --- a/k-local-review.tex +++ b/k-local-review.tex @@ -1180,7 +1180,7 @@ \subsection{Chained Three Body Parity Operators} \conssec \begin{itemize} -\item Does not preserve degeneracy, ground state will retain orginal degeneracy, but excited states will have degeneracy multipled by $n-3$ +\item Does not reproduce the entire spectrum. \item Not very symmetric. \end{itemize} @@ -1206,20 +1206,20 @@ \subsection{Chained Three Body Parity Operators} %\end{equation} \begin{align} -P_\pm(b_1,b_2,b_3;\lambda)=\lambda\left(4\,(b_1b_2+b_2b_3+b_3b_1)+8\,b_a(b_1+b_2+b_3)-12\,b_a-4\,(b_1+b_2+b_3)+3\right)\nonumber \\ +P_\pm(b_1,b_2,b_3)=\left(4\,(b_1b_2+b_2b_3+b_3b_1)+8\,b_a(b_1+b_2+b_3)-12\,b_a-4\,(b_1+b_2+b_3)+3\right)\nonumber \\ \mp (2\,b_1+2\,b_2+2\,b_3 +4\,b_a-5). \end{align} This can be written more compactly in terms of $z$: \begin{equation} -P_\pm(z_1,z_2,z_3;\lambda)=\lambda\left(z_1z_2+z_2z_3+z_3z_1+2z_a(z_1+z_2+z_3)\right)\mp (z_1+z_2+z_3 +2z_a). +P_\pm(z_1,z_2,z_3)=\left(z_1z_2+z_2z_3+z_3z_1+2z_a(z_1+z_2+z_3)\right)\mp (z_1+z_2+z_3 +2z_a). \end{equation} Using three copies of this 3-local gadget as a building block, and using two additional auxilliary variables, the spectrum of the 5-local term $z_1z_2z_3z_4z_5$ can be reproduced by the following Hamiltonian \begin{equation} -H_{2-\rm{local}}=P_+(b_1,b_2,b_{a_1};\lambda)+P_+(b_{a_1},b_3,b_{a_2};\lambda)+P_+(b_{a_2},b_4,b_5;\lambda). +H_{2-\rm{local}}=P_+(b_1,b_2,b_{a_1})+P_+(b_{a_1},b_3,b_{a_2})+P_+(b_{a_2},b_4,b_5). \end{equation} \refsec From aac50343f2c4e32487abde31ba876de07760be17 Mon Sep 17 00:00:00 2001 From: Nick Chancellor Date: Wed, 16 May 2018 16:54:06 +0100 Subject: [PATCH 2/3] P_+ changed to P_- --- k-local-review.pdf | Bin 386569 -> 386569 bytes k-local-review.tex | 2 +- 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/k-local-review.pdf b/k-local-review.pdf index 3a90c014c3f126651bdcf69755ac5f1dc232c54c..ed176b18e3c06eae77e1d14a5ac6896691765f15 100644 GIT binary patch delta 301 zcmeA?Bi?yNe8buW^ZxY z?o**z^LKleKb^i@Bl@d&@2PH^$DdcZO|7r5srYOk{dA*ubLhhM(1naZ%ml>DK+Li| zbRnyd8LOG8v9a0ooa?M|5a#y&>#Wn*oL!xb-JBhr9Zif}oh=QGEF7H-T+LkE44jOe V%#94q%UY1ij3(uMQ(6#Zi<@;zB;wpUWJ`sOC( zBiq^Q4>_+>?|I-q<>39ot#h;Fd2fW@yIUiE_OV86Uh~;kJNHWoUc1_%=~Aw`Aim_Q z>r<_*=kG4r{pob@l(oOQ-JZJ6`&b#e_|$%TyFEYUr(|vnZw_799=ebbh?#(x8Hic7 zhc09lGGjG0F)=Zno^zd54#M2tf1Pz2o3ojjrHQkFsf(qti Date: Thu, 17 May 2018 10:22:55 +0100 Subject: [PATCH 3/3] references and other changes to LZL --- k-local-review.pdf | Bin 386569 -> 386269 bytes k-local-review.tex | 6 ++++-- 2 files changed, 4 insertions(+), 2 deletions(-) diff --git a/k-local-review.pdf b/k-local-review.pdf index ed176b18e3c06eae77e1d14a5ac6896691765f15..c18e41347e5a72009957a92afb08cb7db0ea5830 100644 GIT binary patch delta 38464 zcmZVlQ*@wB6SfV!XJXs7zx#Q=9~w=2@8q6u@xLYKOD21nVp5pZxS{xcCI8PB^uyTSKfP_3$6QD 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